US-backed forces trying to oust Islamic State militants from the Syrian city of Manbij took "almost complete control" of the city on Saturday, the Syrian Observatory for Human Rights said.

The Syria Democratic Forces (SDF), which includes the powerful Kurdish YPG militia and Arab fighters, launched its campaign two months ago with the backing of US special forces to drive Islamic State from a last stretch of the Syrian-Turkish frontier.

The official spokesman of the SDF-allied Manbij military council, Sharfan Darwish, told Reuters that battles were continuing but that around 90 per cent of the city had now been cleared of Islamic State.

Pockets of militants are still present in the centre of the city, the Britain-based Observatory said.

On July 31 2016 US forces claimed to have seized control of almost 70 per cent of Manbij after making rapid advances in the previous two days.

The SDF had pushed back the ultra hardline Sunni militants into the old quarter after seizing most of the western, eastern and southern sectors of the city, Sharfan Darwish of the SDF-allied Manbij military council told Reuters.

"They are now mainly in the old quarter of the city and parts of the north-eastern part of the city," Darwish added.

Though at least 2,300 civilians have been able to escape from Manbij, thousands of residents are still trapped inside. The presence of civilians, who the militants were trying to stop from leaving, was hampering US air attacks, Kurdish sources said.

Progress in storming the city had also been slowed by militants using snipers and planting mines, the Kurdish sources said.

Manbij's loss would be a huge blow to the militants since it is a vital conduit for the transit of foreign jihadists and provisions from the Turkish border.

"The military initiative is in our hands and the campaign is now being undertaken to liberate what is left of the city and progress is continuing until this moment," Darwish said.

Manbij is in the northern province of Aleppo, which forms a theatre for several separate battles between multiple warring sides in Syria's five-year-old conflict.