US Defense Secretary Jim Mattis said yesterday the United States would closely examine proposed de-escalation zones aimed at easing Syria's civil war but warned "the devil's in the details" and that much needed to be worked out.

The deal to create "de-escalation" zones in the major areas of conflict in western Syria took effect on Saturday.

The initiative was proposed by Russia, President Bashar al-Assad's most powerful ally, with the support of Turkey, which backs the opposition. Iran, Assad's other major ally, also backed it.

Political and armed opposition groups have rejected the proposal, saying Russia has been unwilling or unable to get Assad and his Iranian-backed militia allies to respect past ceasefires.

Syrian Foreign Minister Walid al-Moualem said yesterday that his government would abide by the terms of the plan so long as rebels also observed it, although the Syrian government has also said it will continue to fight what it calls terrorist groups, reported Reuters.

Russia said yesterday it had tabled a draft resolution at the United Nations Security Council to back up a deal on establishing safe zones in Syria.

"We confirm that a draft resolution has been introduced," Russian news agencies cited the country's UN mission spokesman Fyodor Strzhizhovsky as saying in New York, without giving details.

A source at the UN told Russia's Interfax news agency that "a vote on the draft will take place possibly this week".

Meanwhile, Syrian rebels and their families began evacuating from a district of Damascus for the first time yesterday, bringing the government closer to recapturing all of the capital.

The evacuation began days after regime backers Russia and Iran and rebel supporter Turkey signed a deal to implement "de-escalation zones" where the government and opposition will halt hostilities, reported AFP.