Elite Iraqi forces engaged in "intense" fighting with jihadists in eastern Mosul Saturday, an officer said, as civilians who had been trapped by the fighting sought to flee the city.

Iraqi forces launched a massive operation to retake the country's second city from the Islamic State group on October 17, and the Counter-Terrorism Service (CTS) special forces have pushed the jihadists back from some Mosul neighbourhoods.

In neighbouring Syria, the US-backed Syrian Democratic Forces (SDF) said they were making progress towards Raqa, the other remaining city in the cross-border "caliphate" that IS declared two years before.

But there are still weeks if not months of fighting ahead in Mosul, and Raqa may take even longer, with the SDF saying it is still some 30 kilometres (18 miles) from the city.

"The fighting is intense this morning. We're trying to fortify our positions in Arbajiyah before continuing our attack into Al-Bakr," said CTS Staff Lieutenant Colonel Muntadhar Salem, referring to two Mosul areas.

Salem later clarified that the aim was to surround Al-Bakr but not to assault it for now.

Staff Lieutenant Colonel Ali Fadhel also confirmed that objective, saying: "We... are advancing towards Al-Bakr so that we can surround it."

"There were three car bombs coming out from Al-Bakr toward our positions that we spotted with our drone and hit with our tanks," Salem said.

The jihadists are also using drones for observation, one of which was shot down by CTS forces, Fadhel said.

The gun and mortar fire in the city lessened in intensity as the day wore on, though there was still some sniper fire in the afternoon.

- Trapped for 10 days -

As fighting raged deeper in the city, civilians, some of them carrying white flags, walked toward its outskirts, gathering near an Iraqi military truck that would take them out of the city to safety.

In the Arbajiyah area, CTS escorted a group of about two dozen civilians, some of them wounded, away from the front line.

"We've been stuck for 10 days," Luay Abdelqader Mohammed, a resident of Arbajiyah, told AFP.

"Today, these guys came and we called out to them. We put up the white flag and they got us out," Mohammed said, referring to CTS forces.

"Eight of my family members were wounded in the fighting, but (CTS) treated us here. I'm going to try to get out and go to Baghdad, and we'll only return if the situation here calms down," he said.

More than 49,000 people have now been displaced since the Mosul operation began, the International Organization for Migration said on Saturday.

Aid workers have said that a million or more people could be displaced by the battle for Mosul, meaning that the worst may still be ahead.

In neighbouring Syria, SDF forces have recaptured villages from IS as part of their advance on Raqa, a spokeswoman said.

They were nearing the end of the first phase of the operation, the goal of which is besieging IS in the city, Jihan Sheikh Ahmed told AFP.

"Yesterday six villages and a number of farms and strategic hilltops were liberated," Ahmed said on Saturday.

"We are now 30 kilometres from Raqa," she said.

The Syrian Observatory for Human Rights monitoring group said that at least seven SDF fighters were killed and others wounded in an IS ambush north of Raqa on Thursday, but Ahmed denied that report.