US-backed rebel fighters in eastern Syria said they launched an offensive on Tuesday to sever a vital supply route of the Islamic State group to neighbouring Iraq.

The New Syrian Army's fighters are first aiming to cut the route before targeting Albu Kamal, a town in the oil-rich eastern Deir Ezzor province mostly held by the jihadists.

IS militants seized the town and nearby border crossing in mid-2014, just as the Sunni extremist group declared a self-styled "caliphate" in territory it controlled across both Syria and Iraq.

If the NSA's fighters manage to seize Albu Kamal, it would be the second border point they have captured from the jihadists this year after overrunning Al-Tanaf.

The operation launched on Tuesday is backed by air strikes from the US-led coalition.

Its aim was to "cut Daesh's military supply lines between Syria and Iraq," said NSA spokesman Muzahem al-Sallum, using an Arabic acronym for IS.

"We began our attack in full coordination with the Iraqi side, specifically tribal fighters in Anbar and the counter-terrorism service of the Iraqi government," he told AFP.

Iraqi fighters had launched a parallel operation at noon towards Albu Kamal, which is known as Al-Qaim across the border.

Within hours, units of the NSA were pushing northeast from the Al-Tanaf border crossing and hundreds of its fighters were now locked in clashes with the jihadists, said Sallum.

An online statement published by the NSA asked residents of Albu Kamal to move away from IS positions in the town ahead of coalition air strikes there.

Fighters of the NSA were trained by the British and Americans in Jordan and is backed by the US-led air coalition bombing IS in Syria and Iraq.

The Islamic State group is now facing growing pressure from US-backed offensives on its bastion cities in both Syria and Iraq.

In northern Syria, the Syrian Democratic Forces alliance of Kurdish and Arab fighters have edged into the IS stronghold of Raqa with air cover by coalition warplanes.

In neighbouring Iraq, authorities declared at the weekend that they were fully in control of the city of Fallujah, west of Baghdad.

Fallujah, in Anbar province, was one of the last two cities held by IS in Iraq.

IS has lost the major towns and cities of the province but still controls areas in Anbar's far west, near the Syrian border.