Near Mosul, Iraq (CNN) In the push to free Mosul, Kurdish Peshmerga forces ideally wanted a political plan -- not just a military one -- to help retake the city from ISIS, Iraqi Kurdish President Massoud Barzani said.

"We would have loved to have a political plan along with a military plan, how to manage Mosul, how to administer Mosul, because Mosul has a variety of religions, with ethnicities," Barzani told CNN's Christiane Amanpour on Wednesday.

Iraqi Kurds 'would have loved' political plan for Mosul

Iraqi Kurds 'would have loved' political plan for Mosul 01:46

Iraqi Kurds 'would have loved' political plan for Mosul

But he acknowledged that having one probably "would have taken a longer time."

The operation to free Mosul from two years of ISIS rule marks the first time Kurdish Peshmerga and Iraqi forces have fought against a common enemy, Barzani said.

"We are looking for a good solution for Mosul," he said.

But the battle to free Iraq's second-largest city could be marked with months of bloody fighting.

Attempt to free Christian town

On the road to Mosul, Iraqi-led forces have besieged a Christian town in an attempt to liberate it from ISIS control, but they are facing fierce resistance and exchanging heavy gunfire with militants, a paramilitary general told CNN.

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Iraqi security forces, Peshmerga fighters and a Christian paramilitary group have forced ISIS fighters into the center of Qaraqosh, where airstrikes are pounding the militants, in apparent coalition support of the assault, Gen. Amr Shamoun from the Christian militia group said.

It's the latest clash with ISIS militants in the coalition's aggressive push toward Mosul aimed at unshackling the strategic city from the terror group's brutal control.

The operation has been complicated since ISIS apparently brought civilians into Qaraqosh, which was abandoned after militants took over in 2014.

Part of Qaraqosh has already been liberated, Shamoun said.

Photos: Mosul: Iraqi-led forces push into key city Members of the Iraqi federal police wave the country's flag as they celebrate in the Old City of Mosul on July 9, 2017. Iraq declared victory against ISIS forces in Mosul after a grueling monthslong campaign. The battle to reclaim Mosul, the last major ISIS stronghold in Iraq, has been underway since fall 2016. Hide Caption 1 of 73 Photos: Mosul: Iraqi-led forces push into key city This injured girl was found by Iraqi forces as they advanced against ISIS militants in the Old City of Mosul on Monday, July 3. She was carried away for medical assistance. Hide Caption 2 of 73 Photos: Mosul: Iraqi-led forces push into key city A suspected ISIS fighter is held in a basement while Iraqi forces continue to push for control of the Old City of Mosul on Monday, July 3. Hide Caption 3 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi Special Forces soldier exchanges fire with ISIS militants in the Old City on Friday, June 30. Hide Caption 4 of 73 Photos: Mosul: Iraqi-led forces push into key city A bomb explodes near the al-Nuri mosque complex on Thursday, June 29. Iraq's military has seized the remains of the Great Mosque of al-Nuri. Iraq and the United States have accused ISIS of blowing up the historic mosque. Hide Caption 5 of 73 Photos: Mosul: Iraqi-led forces push into key city Members of the Iraqi Federal Police hold a position as US-led coalition forces advance through the Old City on Wednesday, June 28. Hide Caption 6 of 73 Photos: Mosul: Iraqi-led forces push into key city The remnants of Mosul's ancient leaning minaret are seen in the Old City on Sunday, June 25. ISIS' claim that US warplanes were responsible for the destruction of the minaret is "1,000% false," US officials told CNN. Hide Caption 7 of 73 Photos: Mosul: Iraqi-led forces push into key city Two boys comfort each other after their home collapsed during fighting between Iraqi forces and militants in Mosul on Saturday, June 24. The boys, who are cousins, said some of their relatives were still under the rubble. Hide Caption 8 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi soldier helps transport a girl as residents flee their homes west of Mosul on Friday, May 26. Hide Caption 9 of 73 Photos: Mosul: Iraqi-led forces push into key city Displaced Iraqis make their way through rubble after evacuating their homes in a neighborhood of west Mosul on Wednesday, May 17. Hide Caption 10 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi man tries to extinguish a burning car during fighting in Mosul's western Rifai neighborhood on Tuesday, May 16. Hide Caption 11 of 73 Photos: Mosul: Iraqi-led forces push into key city A member of the Iraqi counterterrorism service secures a building as troops push toward Mosul's Al-Oraibi western district on Sunday, May 14. Hide Caption 12 of 73 Photos: Mosul: Iraqi-led forces push into key city A smoke cloud rises on the front line as the Iraqi Emergency Response Division advances in west Mosul on Saturday, May 6. Hide Caption 13 of 73 Photos: Mosul: Iraqi-led forces push into key city A wounded man is transported in western Mosul on Friday, April 21. Hide Caption 14 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi federal policeman smokes during a break from battle on Wednesday, April 12. Hide Caption 15 of 73 Photos: Mosul: Iraqi-led forces push into key city A member of Iraq's security forces stands guard in eastern Mosul as smoke rises from the ISIS-controlled western section of the city on Friday, April 7. Hide Caption 16 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqis visit a bath house on the southern outskirts of Mosul on Wednesday, April 5. Hide Caption 17 of 73 Photos: Mosul: Iraqi-led forces push into key city Flames billow from an explosion in Mosul during a clash between Iraqi forces and ISIS fighters on Sunday, March 5. Hide Caption 18 of 73 Photos: Mosul: Iraqi-led forces push into key city Families are forced to evacuate as Iraqi forces advance in western Mosul on Thursday, March 2. The number of internally displaced people has surged as the offensive effort has intensified. Hide Caption 19 of 73 Photos: Mosul: Iraqi-led forces push into key city Mosul residents cross a damaged bridge in the al-Sukkar neighborhood on Saturday, January 21. Hide Caption 20 of 73 Photos: Mosul: Iraqi-led forces push into key city French President Francois Hollande and French Defense Minister Jean-Yves Le Drian, right, view territory held by ISIS during a visit to a military outpost near Mosul on Monday, January 2. Hide Caption 21 of 73 Photos: Mosul: Iraqi-led forces push into key city A young girl takes part in a Christmas Day Mass at a church in the predominantly Christian town of Qaraqosh. The area's churches were heavily damaged by ISIS militants before the town was freed by Iraqi forces during the Mosul offensive. Hide Caption 22 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi Shiite fighters ride through a desert area near the village of Al-Boutha al-Sharqiyah, west of Mosul, on Friday, December 2. Hide Caption 23 of 73 Photos: Mosul: Iraqi-led forces push into key city Internally displaced Iraqis who fled the fighting in Mosul watch as a civilian drone films them at the al-Khazir camp on Thursday, December 1. Hide Caption 24 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi soldier searches a home for ISIS militants after Iraqi forces retook the village of Al-Qasr on Wednesday, November 30. Hide Caption 25 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi soldiers transport a comrade who was injured during a battle near the village of Haj Ali on Tuesday, November 29. Hide Caption 26 of 73 Photos: Mosul: Iraqi-led forces push into key city A man mourns during the funeral of four Iraqi paramilitary fighters who were killed in battles in the town of Tal Afar. Hide Caption 27 of 73 Photos: Mosul: Iraqi-led forces push into key city Displaced civilians return to the village of Tall Abtah on Friday, November 25, after Iraqi forces retook the village from ISIS. Hide Caption 28 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi civilians sit on the ground in Mosul on November 24. An Iraqi officer addressed the group, demanding to know the whereabouts of alleged ISIS militants who opened fire on troops a few days earlier. Hide Caption 29 of 73 Photos: Mosul: Iraqi-led forces push into key city An injured baby receives treatment at a field hospital in Mosul on November 15. Hide Caption 30 of 73 Photos: Mosul: Iraqi-led forces push into key city A woman cries Sunday, November 13, after seeing the St. Addai church that was damaged by ISIS fighters during their occupation of the Keramlis village. Hide Caption 31 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi special forces soldier prays next to a Humvee before troops pushed toward Mosul's Karkukli neighborhood on November 13. Hide Caption 32 of 73 Photos: Mosul: Iraqi-led forces push into key city A Kurdish Peshmerga fighter holds part of a defused bomb planted by ISIS militants in Bashiqa, Iraq, on Friday, November 11. Hide Caption 33 of 73 Photos: Mosul: Iraqi-led forces push into key city A member of Iraq's special forces guards two suspected ISIS fighters found hiding in a house in Mosul on November 11. Hide Caption 34 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi woman displaced by war holds her cat near a checkpoint in the Iraqi village of Shaqouli, east of Mosul, on November 10. Hide Caption 35 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi troops watch a broadcast of Donald Trump's acceptance speech in a house in Arbid, on the outskirts of Mosul, on Wednesday, November 9. Iraqi Prime Minister Haider al-Abadi congratulated Trump on his win and said he hoped for continued support in the war on ISIS. Hide Caption 36 of 73 Photos: Mosul: Iraqi-led forces push into key city US Marines install equipment at a coalition base in Qayyara on November 9. Hide Caption 37 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi forces member investigates a mass grave that was discovered after coalition forces recaptured the area of Hamam al-Alil on Monday, November 7. Hide Caption 38 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi children witness a man being interrogated by a member of the Iraqi army at a base next to the Al-Intissar neighborhood of Mosul on November 7. Hide Caption 39 of 73 Photos: Mosul: Iraqi-led forces push into key city A civilian man who fled the fighting trims his beard after reaching an Iraqi army position in Mosul on November 7. Hide Caption 40 of 73 Photos: Mosul: Iraqi-led forces push into key city Children play in debris created by an airstrike in Qayyara on Sunday, November 6. Hide Caption 41 of 73 Photos: Mosul: Iraqi-led forces push into key city Female members of the Freedom Party of Kurdistan sing as they hold a position near Bashiqa on November 6. Hide Caption 42 of 73 Photos: Mosul: Iraqi-led forces push into key city A baby is passed through a fence back to his mother at a refugee camp in the Khazir region on Saturday, November 5. Hide Caption 43 of 73 Photos: Mosul: Iraqi-led forces push into key city People line up to receive food at a refugee camp in the Khazir region on November 5. Thousands are taking refuge in camps set up for internally displaced people. Hide Caption 44 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi soldiers pass near a bridge destroyed in an airstrike in Qayyara on November 5. Hide Caption 45 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi soldiers patrol an alley on the outskirts of Mosul on Friday, November 4. Hide Caption 46 of 73 Photos: Mosul: Iraqi-led forces push into key city A suspected member of ISIS is detained at a checkpoint near Bartella, Iraq, on November 4. Hide Caption 47 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi families pack into a truck to be moved to camps on Thursday, November 3. Hide Caption 48 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi special forces soldier searches for the location of an ISIS sniper in Gogjali on November 1. Hide Caption 49 of 73 Photos: Mosul: Iraqi-led forces push into key city A man fleeing the village of Bazwaya carries a white flag as he arrives at a checkpoint on November 1. Hide Caption 50 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi soldier receives treatment after being injured during clashes with ISIS fighters near Bazwaya on October 31. Hide Caption 51 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi soldier navigates through a shattered windshield as coalition forces advance on Bazwaya on October 31. Hide Caption 52 of 73 Photos: Mosul: Iraqi-led forces push into key city Archbishop Yohanna Petros Mouche, center, performs Mass in the liberated town of Qaraqosh on Sunday, October 30. Hide Caption 53 of 73 Photos: Mosul: Iraqi-led forces push into key city Children play in a camp for internally displaced people near Kirkuk, Iraq, on October 30. More than 600 families from Tel Afar, a town west of Mosul, have been living in the camp since ISIS took control of the area in 2014. Hide Caption 54 of 73 Photos: Mosul: Iraqi-led forces push into key city Displaced families are seen on the road near Qayyara on Saturday, October 29. Hide Caption 55 of 73 Photos: Mosul: Iraqi-led forces push into key city U.S. military personnel take cover in a bunker after a mortar alarm was sounded at a coalition air base in Qayyara on Friday, October 28. Hide Caption 56 of 73 Photos: Mosul: Iraqi-led forces push into key city Women and children grieve over the grave of a family member at a Qayyara cemetery damaged by ISIS on October 27. Hide Caption 57 of 73 Photos: Mosul: Iraqi-led forces push into key city Residents of Qayyara wait for distribution of food and water rations on October 26. Local water sources have been contaminated by the burning oil and sulfur. Hide Caption 58 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraq's counterterrorism forces advance toward ISIS positions in Tob Zawa on October 25. Hide Caption 59 of 73 Photos: Mosul: Iraqi-led forces push into key city Soldiers give first aid to an injured boy in Tob Zawa on October 25. Hide Caption 60 of 73 Photos: Mosul: Iraqi-led forces push into key city Kurdish Peshmerga forces take positions as they start to move toward the Imam Reza and Tizxirab villages of the Bashiqa district on Sunday, October 23. Hide Caption 61 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi forces distribute fruit in the village of al-Khuwayn, south of Mosul, after recapturing it from ISIS on October 23. Hide Caption 62 of 73 Photos: Mosul: Iraqi-led forces push into key city Kurdish security forces detain a suspected member of ISIS in the eastern suburbs of Kirkuk on Saturday, October 22. Hide Caption 63 of 73 Photos: Mosul: Iraqi-led forces push into key city An Iraqi forces member helps a man push a car as they arrive at a refugee camp in Qayyara on October 22. Hide Caption 64 of 73 Photos: Mosul: Iraqi-led forces push into key city Spent bullet cartridges litter the street around the Jihad Hotel, where ISIS militants battled Iraqi security forces in Kirkuk on Friday, October 21. Hide Caption 65 of 73 Photos: Mosul: Iraqi-led forces push into key city Gen. Abdel Ghani al-Asadi, who leads Iraq's counterterrorism forces, sits in Bartella on October 21 after the town was reclaimed. Hide Caption 66 of 73 Photos: Mosul: Iraqi-led forces push into key city Peshmerga fighters look over a village during an assault near Bashiqa on Thursday, October 20. Hide Caption 67 of 73 Photos: Mosul: Iraqi-led forces push into key city Iraqi forces head toward the front lines near Qayyara on Tuesday, October 18. Hide Caption 68 of 73 Photos: Mosul: Iraqi-led forces push into key city A Peshmerga fighter peers up from an underground tunnel in the liberated town of Badana on October 18. ISIS fighters have built tunnels below residential streets to escape from airstrikes. Hide Caption 69 of 73 Photos: Mosul: Iraqi-led forces push into key city Kurdish security forces take up a position near ISIS-controlled villages on Monday, October 17. Hide Caption 70 of 73 Photos: Mosul: Iraqi-led forces push into key city Smoke rises from a suicide car bomb attack carried out by ISIS in the village of Bedene on October 17. Hide Caption 71 of 73 Photos: Mosul: Iraqi-led forces push into key city Members of the Iraqi coalition gather around a fire at Zardak mountain ahead of the offensive. Hide Caption 72 of 73 Photos: Mosul: Iraqi-led forces push into key city Peshmerga forces deploy in the dark near the village of Wardak early on October 17. Hide Caption 73 of 73

Qaraqosh is just one town coalition forces are trying to liberate. The Iraqi army's armored division is closing in on Mosul's fringes after sweeping through enemy-controlled land in two days, freeing communities village by village, the division's commander told CNN on Wednesday.

Recent developments

Lt. Gen. Qassim al-Maliki, commander of the Iraqi 9th armored division, told CNN that in two days:

• The armored division has advanced; it is now three to four miles from the outskirts of Mosul.

• Three brigades have liberated 13 villages to the north and northeast of Quwayr.

• At least 50 ISIS militants and two Iraqi soldiers have been killed, and 25 soldiers injured.

• Dozens of suicide vehicles and a large number of improvised explosive devices have been destroyed.

Marching toward Mosul

In the latest move to oust ISIS, Peshmerga forces launched a "large-scale operation" Thursday northeast of Mosul, the General Command of Peshmerga Forces of Kurdistan Region announced.

According to a statement, the operation will be carried out on three fronts. The advance follows recent gains by Kurdish Peshmerga Forces in east Mosul and advances by Iraqi Security Forces in south Mosul.

Celebrations turn sour

Qaraqosh was a Christian town, home to 50,000 before ISIS took control. An exodus saw thousands flee to Mosul, only to be forced out again when ISIS took that key city.

Iraqi Christians celebrate Tuesday in Irbil after Iraqi forces entered their hometown of Qaraqosh.

Many of those who fled are now living in Irbil, where they celebrated Tuesday when they heard Iraqi forces had entered their hometown.

They held a vigil overnight, holding candles and singing hymns, images showed, while others gathered in the street, cheering and dancing.

But their celebrations may have come too soon. ISIS appeared to be putting up a real fight in Qaraqosh, as the terror group has in several areas since the operation launched Monday.

Displaced Christians from Qaraqosh celebrate in Irbil as Iraqi forces move in to free their hometown.

Another Iraqi military official, speaking on condition of anonymity, told CNN that ISIS fighters have surrounded Iraqi units around the village of Al Absi, near Nimrud, 12 miles (20 kilometers) south of Mosul. The area has seen heavy fighting in the last 36 hours.

Edging closer

Maliki, the Iraqi commander, said his division was around three to four miles (five to six kilometers) from the city's outskirts. He said progress had slowed as protective forces were needed in newly liberated areas to hold ground.

Outside of #Mosul #Iraq armor with Shia flags does not help combat the perception of a sectarian army pic.twitter.com/gRj6NUVyMj — Arwa Damon (@arwaCNN) October 19, 2016

His comments echo those of Sirwan Barzani, a Peshmerga military commander, who told CNN the battle to recapture Mosul could take two months.

Why Mosul matters Since Mosul's capture by ISIS fighters in June 2014, Mosul has been a vital stronghold for ISIS. The largest city under ISIS control in Iraq and Syria, it was the city from which the group first declared the establishment of its so-called caliphate. Since then, ISIS has gradually lost its other Iraqi cities -- Ramadi, Tikrit and Falluja -- to government forces. About 1 million people are estimated to remain in Mosul, once a cosmopolitan trade hub of 2 million residents.

Barzani said it would likely take two weeks for advancing forces to enter the city. Iraq's leaders have said that only Iraqi government troops and national police officers will be allowed to do so amid fears of sectarian retribution, he said.

The coalition's more than 94,000 members vastly outnumber their opponents. But ISIS, expecting the push, has constructed elaborate defenses, including a network of tunnels.

Advancing Iraqi forces sometimes encounter ISIS fighters who seemingly pop out of the ground to fire weapons. The tunnels wind through hills, with one entrance not far from an exit.

Coalition forces will also likely face suicide bombings, car bombs and booby traps.

Up to 5,000 ISIS fighters are in Mosul, a US military official said. ISIS' supporters put the number at 7,000.

A US general said some local ISIS leaders are fleeing.

"We are telling Daesh that their leaders are abandoning them, and we have seen movement out of Mosul," US Army Maj. Gen. Gary Volesky said in a video briefing from Baghdad, referring to ISIS by another name.

ISIS distributed leaflets Wednesday evening to residents, demanding they hand over their mobile phone SIM cards and remove all antennas from the roofs of their homes. ISIS representatives will collect the SIM cards over the next 24 hours, according to the leaflets. Anyone who fails to comply will be arrested, according to the leaflets.

A unit of what appeared to be US special forces advisers entered ISIS territory Monday with the first armored convoy of Peshmerga, a CNN team observed. They followed a dozens-strong unit of Kurdish armor bound for ISIS positions, placing American forces at the front of the fight to retake Mosul.