MOSUL, Iraq (Reuters) - After five months of intense fighting, Iraqi forces have begun to drive back Islamic State into the dense and narrow-alleyed Old City of Mosul, with the mosque where its leader Abu Bakr al-Baghdadi declared a caliphate in 2014 firmly in sight.

Displaced Iraqis flee their homes as Iraqi forces battle with Islamic State militants, in western Mosul, Iraq March 14, 2017. REUTERS/Suhaib Salem

Iraqi leaders say the battle to recapture Mosul is reaching its final stages, trumpeting each gain made against the militants.

But as Islamic State slows Iraqi advances with stiff resistance, residents trapped inside the Old City with the jihadists describe a desperate siege, with widespread hunger, destruction from U.S.-led air strikes, and civilians living in fear of revenge as the ultra-violent group gets cornered.

“If we hadn’t got out this morning, they’d have killed us,” said Hisham Sobhi, 41, who fled with his family from their home on the southwestern edge of the Old City on Thursday.

“They (Islamic State) leave some areas, some homes, but sometimes come back again. If they find people still living in areas considered liberated by the army, they kill them,” he said.

Mosul is many times larger than any other city Islamic State has held in its self-proclaimed Caliphate, and the fight to drive the militants out, which began last October, is Iraq’s biggest ground battle since the U.S.-led invasion of 2003.

Iraqi forces backed by U.S. air power secured the eastern half of the city in January and crossed the Tigris River to fight for the Western side in recent weeks, a decisive battle that would crush the fighters’ sway over territory in Iraq.

Sobhi, speaking at a camp south of Mosul, said militants had managed to return to attack areas that remained insecure after Iraqi forces advanced. The area around his home is roughly along the current front line, which he said could shift either way.

Ghassan Thanoun, Sobhi’s neighbor, said his 8-year-old son had been trapped under rubble in their home, which was severely damaged in an air raid on their block. The boy, who had not been injured, stood silently, traumatized, and looked at the ground.

“We were scared they’d come back - they consider liberated areas infidel, and accuse you of collaborating with the army,” the 50-year-old lawyer said of the Islamic State fighters.

“Yesterday night there was a Daesh attack near the railway station. We didn’t want to hang around any longer,” he said, using an Arabic acronym for Islamic State.

Islamic State has fought fiercely since retreating into the densely-populated Old City.

Counter-attacks under cover of rain have kept the bulk of the forces from Iraq’s elite Rapid Response units and its Federal Police at bay for days on end. Those forces are stationed around the Old City limits and have sent raiding parties to advance on landmarks such as the al-Nuri mosque where Islamic State’s leader Abu Bakr al-Baghdadi proclaimed his caliphate.

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Troops in the elite Counter-Terrorism Service (CTS), operating around the railway station, have also reported difficult fighting in recent days.

NO FOOD, NO WATER

As the battle gets tougher, Iraqi forces have begun to besiege the jihadists. The tightening encirclement is increasing civilian suffering, however, as food cannot get in and medical supplies run low.

“There’s become a siege. There’s no food, no medicine, even in the hospitals,” Thanoun said, adding that he needed urgent treatment for shrapnel wounds from an air strike.

Residents reached by phone still inside the Old City said no food had been brought in for months, and people were surviving on lentils and other basic goods they had stocked.

“It’s been four months that we haven’t eaten fruit and vegetables. The kids ask for just a piece of chocolate, but there are only lentils, and even these are running out,” one resident said, asking to remain anonymous.

A girl in a displaced people’s camp south of Mosul listed the prices of certain goods - $1 equivalent for just one egg, $3 for one cigarette.

Water has also run out. Thanoun and Sobhi said their families had been drinking water from wells.

The encirclement tactics appear to be wearing down Islamic State, however.

“The hospitals are full of wounded fighters,” Thanoun said.

“Wounded civilians as well, but the fighters get priority. They’re treated urgently, by (Islamic State) doctors who include Russians, French, Germans,” he said.

Another resident reached by phone said the militants had deployed snipers and car bombs around the hospitals, and that civilians were no longer being treated.

The Old City is not the only district that Iraqi forces will need to retake, with Islamic State also holed up in a number of areas in the city’s northwest which are traditional Sunni extremist strongholds.

MILITANTS ON THE RUN?

The jihadists had begun to retreat into those areas, witnesses said.

“We see them in all parts of the July 17 district. They’ve taken over schools, mosques, health centers, businesses, and many homes for them and their families to live in,” one resident said.

Another resident of Yarmouk district said Islamic State militants had been going through the area, apparently having fled fighting in the city center, asking for directions to July 17.

Compared to outlying districts, the Old City might yet be the hardest to recapture, with tanks and armored vehicles unable to enter its narrow streets, and IS sniper and mortar fire continuing to rain down on Iraqi forces outside it.

“They withdraw into areas where there are really narrow streets - Bab al-Baydh, Bab al-Jadeed, al-Makkawi, Farouq al-Qadeem, Farouq al-Jadeed,” Thanoun said, listing quarters close to the al-Nuri mosque.

He feared air strikes by the U.S.-led coalition backing Iraqi forces might do great damage to the Old City, as militants hide out in homes, using them as posts to launch sniper and mortar fire.

“When the planes strike, one Daesh dies for every 20 civilians,” he said. “The homes are old, so if an air strike hits, it destroys more than one.”

Inside the Old City, people were just waiting for the offensive to end.

“It’s been raining recently, which in one sense is good because we can gather rainwater for cooking,” a woman reached by phone said, asking to remain anonymous.

“On the other hand, we don’t like it because it stops military operations, and we just want to be done with this war.”