Iraqi forces on Friday entered west Mosul neighborhoods, a key stronghold in the shrinking "caliphate" of the Islamic State group, which replied with deadly suicide attacks in Iraq and Syria.

As the war on the world's most violent jihadist group escalated, Iraqi warplanes struck IS militants inside neighboring Syria, a first that Damascus said was coordinated between the two governments.

In yet another key landmark in the bloody offensive to retake Mosul, the largest city ever held by the jihadists, elite Iraqi forces punched into districts of the west bank for the first time.

The interior ministry's elite Rapid Response force, which retook Mosul airport on Thursday, kept its momentum and broke into the adjacent Jawsaq neighborhood.

They were met by mortar fire and snipers but also by ululating women celebrating the end of more than two and half years of tyrannic rule and by men begging for cigarettes.

"I don't have any left, I swear, I don't have any left," said one government fighter as his convoy advanced slowly down the street.

The elite Counter-Terrorism Service that did most of the fighting in the four-month-old Mosul offensive entered a neighborhood further west along the city's southern limits.

"We entered the outer edge of Al-Maamun neighborhood," said Staff Lieutenant General Abdul Wahab al-Saadi, a top CTS commander.

- 'Moving fast so far' -

"IS is using vehicle bombs -- this morning three were destroyed. We have some injuries from the weaponized drones and mortars," he told AFP just south of Mosul.

It was not immediately clear whether Iraqi forces would keep venturing deeper into west Mosul or consolidate their positions on the edges ahead of dangerous operations towards the center.

The fight "has moved very fast so far but we'll see what happens in the next stage. It might be more difficult," Saadi admitted.

The narrow streets of the Old City, home to the mosque where Abu Bakr al-Baghdadi made his only public appearance as IS leader and proclaimed the "caliphate" in July 2014, could become a death trap.

They will be impassable for some military vehicles, forcing Iraqi forces to go on dismounted raids. IS has covered some streets with roofs to block aerial surveillance.

The loss of west Mosul would be a death blow to the jihadists' claim they are running a "state" and leave the city of Raqa in neighboring Syria as the only major urban center they still control.

IS still holds scattered pockets of territory across Iraq and Syria but has suffered a string of setbacks in the past year and over the past few hours also lost their last bastion in Syria's Aleppo province.

Turkey said Friday its troops and the Syrian rebels it backs had fully retaken the town of Al-Bab after weeks of fierce IS resistance, but the jihadists replied with a deadly suicide bombing there, killing 51 people.

IS claimed the attack outside Al-Bab, in Susian.

- Syria bombing -

"Al-Baghdadi's dogs could not bear their huge loss, and their suicide bombers have begun to take revenge," said field commander Abu Jaafar of the Mutasem Brigades.

After a lightning advance, the rebels became mired in a drawn-out conflict in Al-Bab which proved to be the bloodiest fight in Turkey's campaign, where Ankara suffered most of its 71 losses thus far.

An IS suicide bomber driving an explosives-laden vehicle and gunmen also attacked an Iraqi position near Jordan Friday, killing at least 15 border guards, officials said.

IS has lost most towns in its traditional western Iraqi bastion of Anbar province but still has desert hideouts from which it continues to harass the security forces.

Friday's raid was the deadliest to date against the border guard.

For three years jihadists have crossed the Iraq-Syria border unimpeded, but on Friday it was the Iraqi government that carried out its first cross-border air strike.

Prime Minister Haider al-Abadi announced that the air force struck targets on the Syrian side of the border, in Albu Kamal and Husseibeh areas.

- Cross-border strike -

The target was IS militants the Joint Operations Command said were responsible for car bombings in Baghdad last week, including one that killed 52 people.

A source close to Syria's foreign ministry told the pro-regime newspaper al-Watan that the strike was conducted "in full coordination" with Damascus.

"We are determined to track down terrorists trying to kill our sons and citizens wherever they are," said Abadi, who has met top U.S. defense officials all week, including Pentagon chief Jim Mattis when he visited Baghdad.

A Pentagon spokesman said Friday the U.S. had provided intelligence to help the Iraqis in the strike.

The 60-nation coalition dominated by the United States has carried out more than 10,000 strikes on IS targets since 2014, and recently stepped up its involvement to help Baghdad retake Mosul.

Forces on the ground officially in an advisory capacity have increasingly been involved in combat and have been more visible than ever on the front lines since the push on west Mosul began on February 19.

Abadi urged his forces to exercise the utmost caution when retaking west Mosul, where the United Nations believes around 750,000 civilians are trapped with dwindling food and medical supplies.