An alliance of US-backed fighters says it has begun a new phase of its campaign on the ISIL-held city of Raqqa in northern Syria, aiming to complete its encirclement and sever the road to the group's strongholds in Deir Az Zor province.

The Syrian Democratic Forces (SDF) said in a statement on Saturday that the offensive was getting an "increasing support from the international coalition forces through guaranteeing air cover for our forces' advances or via the help provided by their special teams to our forces on the battle ground".

The multi-ethnic SDF alliance, which is dominated by the Kurdish YPG fighters, is waging a campaign to capture the Islamic State in Iraq and the Levant (ISIL, or ISIS) group's stronghold in Raqqa, with support from the US-led coalition against the group. The SDF also includes Arab factions, Syrian Christian fighters and Turkmen units.

According to Kurdish media, SDF spokesperson Jihan Sheikh Ahmed said they started a new phase to liberate the villages in the east part of Raqqa, with the support of civilians from the region.

Al Jazeera's Stefanie Dekker, reporting from the Turkish city of Gaziantep along the Syrian border, said that the offensive was initially launched in November last year and was being conducted in phases.

"The first phase was pushing from the north. Second one was pushing from the west. And now, in the third phase, the forces are trying to push from the east," she said.

"There is also heavy fighting that has been going on north of Raqqa city, where the SDF are backed by coalition air strikes.

"Also overnight, the coalition forces took out the last bridge crossing the Euphrates. There were five bridges and all of them were taken out."

Point of tension with Turkey

All the parties that participated in the first two phases of the offensive will take part in this phase, according to the SDF.

Several hundred US Special Forces soldiers have been supporting the SDF operations against ISIL in northern Syria. France said in June that its special forces were advising rebels in the same area.

OPINION: US alliance with Syrian PYD alienates Turkey

US support for the SDF has been a point of tension with NATO ally Turkey, which views the YPG as an extension of the Kurdistan Workers' Party (PKK), a group that has fought the Turkish state for three decades now.

The US says it is providing training and material support to Arab elements of the SDF only. It supplied them last month with armoured vehicles for the first time to help in the Raqqa campaign.

US President Donald Trump signed an executive order last week requesting the Pentagon, joint chiefs of staff and other agencies to submit a preliminary plan in 30 days for defeating ISIL.

One key decision awaiting the Trump administration is whether to directly provide weapons to the YPG.