A US warplane shot down a Syrian army jet on Sunday in the southern Raqqa countryside, with Washington saying the jet had dropped bombs near U.S.-backed forces and Damascus saying the plane was downed while flying a mission against Islamic State militants.

A Syrian army statement released on Syrian state television said the plane crashed and the pilot was missing in the first such downing of a Syrian jet by the United States since the start of the conflict in 2011.

The army statement said it took place on Sunday afternoon near a village called Rasafah.

The "flagrant attack was an attempt to undermine the efforts of the army as the only effective force capable with its allies ... in fighting terrorism across its territory," the Syrian army said.

"This comes at a time when the Syrian army and its allies were making clear advances in fighting the Daesh (Islamic State) terrorist group," it added.

The U.S. Central Command later issued a statement saying the Syrian plane was downed "in collective self-defence of Coalition-partnered forces," identified as fighters of the Syrian Democratic Forces (SDF) near Tabqah.

It said that "pro-Syrian regime forces" had earlier attacked an SDF-held town south of Tabqa and wounded a number of fighters, driving them from the town.

Coalition aircraft in a show of force stopped the initial advance. When a Syrian army SU-22 jet later dropped bombs near the U.S.-backed forces, it was immediately shot down by a U.S. F/A-18E Super Hornet, the statement said.

Before it downed the plane, the coalition had "contacted its Russian counterparts by telephone via an established "de-confliction line" to de-escalate the situation and stop the firing."

The coalition does "not seek to fight the Syrian regime, Russian or pro-regime forces" but would not "hesitate to defend itself or its "partnered forces from any threat," the statement said.

The U.S.-led coalition has in recent weeks escalated its aerial bombing campaign in northern Syria and Raqqa province. U.S.-backed forces have encircled the city of Raqqa and captured several districts from the militants.

The Syrian army, which has been taking territory from retreating Islamic State militants in the eastern Aleppo countryside, has moved into Raqqa province and seized back some oil fields and villages that had been under the militants' control for almost three years.

An SDF official told Reuters the Syrian army had been engaged in skirmishes in recent days with U.S.-backed forces near the town of Maskaneh close to the borders of Raqqa province, much of which is now held by U.S.-backed groups fighting Islamic State.

The Syrian army backed by Iranian-backed militias has also been in competition in southeastern Syria with U.S.-backed Free Syrian Army (FSA) rebels who are also trying to recapture territory from Islamic State.

On several occasions in recent weeks, warplanes of the U.S.-led coalition have also struck pro-government forces to prevent them advancing from a U.S.-controlled garrison in southeastern Syria at a spot where the country's borders join with Iraq and Jordan.

Washington also described those strikes as self-defence.