President Bashar al-Assad rejected the creation of safe zones for refugees and displaced people in Syria, an idea supported by U.S. President Donald Trump, according to a transcript from an interview with Yahoo News released on Friday.

He signalled he would welcome cooperation with Washington in the fight against Islamic State, however, as long as the United States took a "clear political position" on Syria's sovereignty and unity.

Assad has cautiously welcomed the new U.S. administration's focus on fighting the jihadists, in which Trump has held out the possibility of cooperation with Damascus ally Russia.

Under former U.S. President Barack Obama, the United States called for Assad's departure and supported rebels fighting to unseat him.

The Syrian government has rejected the creation of safe zones, favoured by rebel backers including Qatar, which could ratchet up U.S. military involvement in Syria.

"It's not a realistic idea at all," Assad said in the transcript. "This is where you can have natural safe zones, which is our country. They don't need safe zones at all."

"It's much more viable, much more practical and less costly to have stability than to create safe zones."

Assad said safe zones would be at risk of attack from armed groups.

The United Nations also rejects safe zones, saying conditions in Syria, where battles rage on between multiple sides, are not suitable.

Trump has not provided details about the proposed safe zones, except to say he would have the Gulf states pay for them.

Much of the conflict is focussed on a number of separate battles being waged against Islamic State: by Russian-backed Syrian government forces and their allies, U.S.-backed Kurdish and Arab fighters, and Turkish-backed Syrian insurgents.

The United States has deployed special forces to Syria to support the Kurdish YPG militia and its allies, and not in coordination with the Syrian army.

Fight against islamic State

Assad said U.S. troops would be "welcome" in Syria to fight Islamic State provided Washington coordinate with Damascus and recognise the sovereignty of his government.

"If the Americans are genuine, of course they are welcome. Like any other country, we want to defeat and to fight the terrorists," he said

"Troops is part of the cooperation ... (but) you cannot talk about sending troops ... if you don't have a clear political position towards not only the terrorism, towards the sovereignty of Syria, towards the unity of Syria," he said.

"It must be through the Syria government."

Moscow said Trump and Russian President Vladimir Putin had discussed setting up "genuine coordination" in the fight against Islamic State and "other terrorist groups" in Syria during a phone call last month.

There has been no indication the United States would coordinate with Syria itself.

For now, U.S.-Russian cooperation is largely limited to ensuring that the two countries' air forces operate safely and that the risk of accidental confrontation or collision is minimised.

Assad also dismissed a report by Amnesty International which said up to 13,000 prisoners had been executed at a military jail in Damascus since 2011.

World powers involved in the Syrian conflict have pushed diplomatic efforts to end the war, which has killed hundreds of thousands of people and created millions of refugees.

Assad repeated that he would leave power if voted out by the Syrian people, and would consider an early presidential election after parliamentary polls are held.