Iraqi special forces were poised to assault one of the Islamic State of Iraq and the Levant (ISIL) group's most emblematic bastions, Fallujah, as the group counter-attacked in both Iraq and neighbouring Syria.

The fighting on Sunday prompted a new exodus of thousands of desperate civilians from the surrounding areas and deep concern for the many more trapped in the battlegrounds.

The overall commander of the Fallujah operation, Abdelwahab al-Saadi, said on Saturday it was a matter of hours before the Counter-Terrorism Service (CTS) entered the city.

The week-old operation has so far focused on retaking villages and rural areas around Fallujah, which lies just 50 kilometres west of Baghdad.

"I won't tell you hours but the breach of Fallujah will happen very soon," Hadi al-Ameri, a senior commander in the Hashed al-Shaabi paramilitary force, told Iraqi television.

CTS's involvement will mark the start of a phase of urban combat in a city where US forces in 2004 fought some of their toughest battles since the Vietnam War.

In Iraq, only a few hundred families managed to slip out of the Fallujah area, with an estimated 50,000 people still trapped inside the city proper.

According to the Norwegian Refugee Council (NRC), around 3,000 people have managed to escape the Fallujah area since May 21.

The biggest wave so far arrived on Saturday night, NRC said, but a larger influx could be triggered when the urban battle between CTS and ISIL begins in earnest.

"Our resources in the camps are now very strained, and with many more expected to flee we might not be able to provide enough drinking water for everyone," said Nasr Muflahi, NRC's Iraq director.

"We expect bigger waves of displacement the fiercer the fighting gets."

The Fallujah operation has come at a human cost, rights groups said, amid battles between ISIL (also known as ISIS) fighters and the advancing Iraqi army and allied Shia militia.

Al Jazeera's Omar al-Saleh, reporting from Erbil in northern Iraq, described the situation in the city as dire.

"There is a lack of medicine and food. They are caught in the fighting between ISIL and Iraqi forces," he said.

Peshmerga offensive

The ISIL fighters were also under pressure from Kurdish fighters east of their northern Iraqi stronghold Mosul and from US-backed Kurdish-led fighters in Syria.

Iraq's autonomous Kurdish region on Sunday announced the launch of a pre-dawn offensive involving 5,500 Peshmerga fighters to retake an area on the road between its capital Arbil and Mosul.

"This is one of the many shaping operations expected to increase pressure on ISIL in and around Mosul in preparation for an eventual assault on the city," the Kurdistan Region Security Council said in a statement.

Ten hours into the operation, which was launched a day after a wave of 12 coalition air strikes in the area, Kurdish forces had fully retaken three villages, it said.


READ MORE: Iraqi Kurds - 'Losing to ISIL is not an option'


In Syria, Kurdish rebels from the People's Protection Units (YPG) allied to Arab fighters and backed both on the ground and in the air by the US-led coalition, were targeting Raqqa, ISIL's de facto Syrian capital. 

ISIL countered in both countries where they declared their "caliphate" in 2014, attacking rebels in Syria as well as the Iraqi town of Heet, which the army recaptured just last month.

"An attack by Daesh (ISIL) terrorists on several parts of Heet was thwarted ... Now the whole area is under control," the Joint Operations Command said in a statement.

Suicide attack

It said coalition aircraft targeted ISIL forces during the attack and added that pockets of ISIL fighters remained.

"Daesh attacked Heet to ease the pressure on their fighters inside Fallujah, especially following the announcement that CTS had arrived," the statement said.

Northeast of Baghdad on Sunday, police said a suicide bomber killed at least seven people and wounded 22 when he blew himself up in a cafe in Muqdadiyah, in an attack claimed by ISIL.

In northern Syria, ISIL has launched an offensive against the towns of Marea and Azaz that threatens to overrun the last swath of territory in the east of Aleppo province held by rebels.

It would also bring ISIL to the doorstep of the Kurdish enclave of Afrin.

Iraqi forces surround Fallujah as they push to drive out ISIL

As the fighting raged on multiple fronts, civilians were once again bearing the brunt of the conflict.

At least 29 civilians have been killed since ISIL began the assault in Aleppo province early on Friday, the Syrian Observatory for Human Rights said.

More than 6,000 civilians fled into the countryside, it said.

Northwest of Azaz, a senior nurse said late on Saturday that a hospital supported by Doctors Without Borders (MSF) was closed except for emergencies.

MSF said on Friday it was evacuating patients and staff from the hospital in Salamah town as it was just 3km from the frontline.

Source: Al Jazeera and agencies