MOSUL, Iraq/RAQQA, Syria (Reuters) - U.S.-backed Iraqi forces pressed Islamic State fighters holding out in Mosul’s Old City on Friday, while in Syria the militant group launched a counter-attack against an alliance of militias trying to oust it from its de facto capital of Raqqa.

Members of the Counter Terrorism Service pose for a picture with an Iraqi flag in front of the ruins of Grand al-Nuri Mosque at the Old City in Mosul, Iraq, June 30, 2017. REUTERS/Alaa Al-Marjani

In Iraq, dozens of civilians poured out of Mosul, long held by IS, and fled in the direction of the Iraqi forces, many of them women and children, thirsty, tired and some wounded.

Iraqi authorities say they are only days away from a victory over militants in their remaining redoubt in Mosul, though commanders of counter-terrorism units fighting their way through the narrow streets of the Old City say die-hard IS fighters are dug in among civilians and the battle ahead remains challenging.

Across the border in Syria, parts of which the IS says fall under its self-proclaimed caliphate, the picture was more complex.

The Syrian Observatory for Human Rights, a Britain-based war monitor, said the group had retaken most of the industrial district of Raqqa after mounting a fierce counter-attack against the Syrian Democratic Forces (SDF), a U.S.-backed alliance of Kurdish and Arab militias.

But west of Raqqa, the Syrian army put the group under more pressure, driving it from its last territory in Aleppo province, a Syrian military source said, in a strategically-important move that relieves pressure on a government supply route.

Even though the IS group is under pressure in these urban strongholds in Iraq and Syria its fighters still occupy an area as big as Belgium across the two countries, according to one estimate.

THOUSANDS DISPLACED, KILLED

In Iraq, grinding warfare in Mosul has displaced 900,000 people, about half the city’s pre-war population, and killed thousands of civilians, according to aid organizations.

Major General Maan al-Saadi, of the Counter Terrorism Service, told Reuters it could take four to five days to capture the insurgents’ redoubt in Mosul by the Tigris River which was defended by about 200 militants.

Tens of thousands of civilians are trapped in the city in desperate conditions, with dwindling supplies of food, water or medicine and no access to health services, according to those who have managed to flee.

The capture of the city would in effect mark the end of the Iraqi half of the caliphate, although the group still controls territory west and south of the city, holding sway over hundreds of thousands of people.

Those who escaped on Friday streamed through alleyways near the Grand al-Nuri Mosque, where IS leader Abu Bakr al-Baghdadi declared the caliphate in 2014 and which Islamic State fighters blew up a week ago rather than see it fall to the Iraqi army.

Iraqi Prime Minister Haider al-Abadi declared the end of the caliphate on Thursday after CTS units captured the ground of the ruined 850-year-old mosque.

A Reuters correspondent on Friday saw smoke billowing over the riverside districts amid artillery blasts and burst of gunfire. Western troops from the U.S.-led coalition were helping adjust artillery fire with air surveillance, he said.

BATTLE FOR RAQQA

The SDF, the U.S. backed alliance in Syria, took the industrial district of Raqqa this month in its biggest gain so far in its fight for IS’s Syrian capital and if, as the Observatory has reported, IS has regained control there it would be a setback.

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The SDF, on its social media feed, acknowledged there had been intense clashes, but added that the whole industrial district was still in its hands and the attack had been thwarted.

Equally, IS appeared to have suffered a setback in Syria with the army taking the last stretch of the Ithriya-Rasafa road, part of the highway from Hama to Raqqa, forcing IS fighters to withdraw from a salient it held to the north, a Syrian military source and the Observatory said.

Islamic State had used that salient, an area containing a range of hills and a dozen villages, to mount frequent attacks on a different road linking Ithriya to Khanaser, part of the government’s only available land route to Aleppo.

The capture of the Ithriya-Rasafa road also shortens the Syrian army’s route to its battlefront with Islamic State south of Tabqa, a possible route for its multi-pronged offensive to relieve the government’s enclave in Deir al-Zor.

On Thursday, the Observatory said the SDF had managed to take the last stretch of the Euphrates’ south bank opposite Raqqa, completely encircling Islamic State inside the city.

Since all Raqqa’s bridges were already destroyed, and the U.S.-led coalition was striking boats crossing the river, the city had already been effectively isolated since May.

The secretive Baghdadi, who has scarcely been seen publicly since proclaiming the caliphate, has left the fighting in Mosul to local commanders and is believed to be hiding on the Iraq-Syrian border, according to U.S. and Iraqi military sources.

He has often been reported killed or wounded. Russia said on June 17 its forces might have killed him in an air strike in Syria. But Washington says it has no information to corroborate such reports and Iraqi officials have also been skeptical.

(For a graphic of battle for Mosul, click tmsnrt.rs/2rEoDr4)