WASHINGTON (Reuters) - Despite saying that the Syrian government is not doing enough to stop Islamic State militants from moving through its territory, the U.S.-led coalition fighting the group does not intend to target militants in those areas, a senior coalition official said on Wednesday.

The comments by British Army Major General Felix Gedney indicate that the coalition will rely on the Syrian government to go after Islamic State militants in areas controlled by forces loyal to Syrian President Bashar al-Assad.

U.S. officials have said in the past that the Syrian government forces are too few, too poor and too weak to fight Islamic State.

Gedney, the deputy commander of strategy and support for the coalition, said the fight against Islamic State was not over, and militants had been seen moving west of the Euphrates river.

“They seem to be moving with impunity through regime-held territory, showing that the regime is clearly either unwilling or unable to defeat Daesh within their borders,” Gedney said, using an Arabic acronym for the militant group.

Syrian government forces and their allies, backed by Russian air power, are mostly on the western side of the Euphrates, while forces backed by the coalition are on the eastern bank.

When asked whether the coalition will target the militants in areas controlled by the Syrian regime, Gedney said they did not plan to.

“We will continue to deconflict with the Russians, but we have got no intention to operate in areas that are currently held by the regime,” Gedney said.

Russia and the United States have set up a communications channel to reduce the chance of fighting between the two rival campaigns against Islamic State.

“We would call on the Syrian regime to clear ISIS from those areas that are currently under their control,” he added.

The coalition estimates that fewer than 1,000 Islamic State fighters remain in Iraq and Syria.

Iraq and Syria have both declared victory over Islamic State in recent weeks, after a year in which the two countries’ armies, a range of foreign allies and various local forces drove the fighters out of all the towns and villages that once made up the militant group’s self-proclaimed caliphate.

U.S. Defense Secretary Jim Mattis has said the U.S. military will fight Islamic State in Syria “as long as they want to fight.” He said the U.S. military’s longer-term objective would be to prevent the return of an “ISIS 2.0.”