Hundreds of Syrian fighters have begun to leave the besieged Damascus suburb of Barzeh as part of an evacuation deal reached with the government, according to state television and a war monitor.

State-run Ekhbariya television cited its reporter there as saying the evacuation of fighters from Barzeh for the rebel-held Idlib province had begun to be implemented on Monday, but without giving further details.

Idlib, a mostly rural province in northwest Syria abutting the Turkish border, is a major opposition stronghold.

"Armed men and some of their families have begun leaving Barzeh on 40 buses heading towards northern Syria," the channel said in a news alert.

An AFP news agency photographer in Barzeh saw rebel fighters carrying light weapons looking on as children and women in brightly coloured headscarves pulled shabby suitcases and duffel bags.

The Syrian Observatory for Human Rights, the Britain-based war monitor, reported that buses had arrived in Barzeh at dawn and a group of hundreds of fighters and their family members had started to board.

The Barzeh evacuation deal was struck late on Sunday night, and dozens of people had gathered in the district from the morning.

The Syrian Observatory said that more people would leave Barzeh over the coming days as part of the same deal.

A source from the pro-government National Defence Forces said rebel fighters would be allowed to take their "personal weapons" with them.

They are the first evacuations from Damascus in the country's six-year war.

Al Jazeera's Charles Stratford, reporting from Gaziantep in neighbouring Turkey, said armed opposition groups have been highly critical of these evacuation plans and accuse the government of using them as a form of "ethnic cleansing".

READ MORE: Syria's civil war explained from the beginning

"It's a start today, but there are huge questions ... about how the opposition forces will respond to the de-escalation plan," he said.

Barzeh, near the rebel-held Eastern Ghouta district of towns and farms, has been the site of intense fighting between rebels and the Syrian army in recent months.

Assad's government controls all but six districts of Damascus: Barzeh, Qabun, Jobar, Tishrin, Tadamun, and the Palestinian refugee camp of Yarmouk.

Fouaa and Kefraya

A military media unit run by the armed Lebanese Shia armed group Hezbollah, an ally of the Syrian government, reported on Monday that several Red Crescent ambulances had also arrived at the rebel-besieged towns of Fouaa and Kefraya near Idlib.

Those were part of a mutual evacuation deal that included two towns besieged by government forces and involved exchanging thousands of people between the warring sides last month.

Syrian President Bashar al-Assad has promoted the use of such evacuations, along with what his government calls "reconciliation" deals for rebel-held areas that surrender to the government, as a way of reducing bloodshed.

However, the UN has criticised both the use of siege tactics which precede such deals and the evacuations themselves as amounting to forcible displacement.

Many of those who have left other besieged areas of Syria have also relocated to Idlib, a mostly rural province abutting the Turkish border which is a major rebel stronghold.

Negotiations were ongoing for a similar deal in the district of Qabun, in Damascus's northeast, which has seen fierce shelling for weeks by forces loyal to the Syrian government.

'De-escalation process'

The deal follows Saturday's start of a "de-escalation process" put in place by government allies Russia and Iran and rebel-backer Turkey in four regions of Syria - but not the capital itself.

It mandates an end to hostilities, including air strikes, in specified zones for six months.

The deal came into effect on midnight Friday, with fighting subsiding, but the co-sponsors have until June 4 to submit maps finalising the borders of the zones.

READ MORE: Syria's 'de-escalation zones' explained

It calls for continued fighting against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), which is largely absent from the areas where the zones will be implemented, as well as former al-Qaeda affiliate Fateh al-Sham Front, which is active in all four proposed areas..

The deal says that the "de-escalation zones" would be bordered by security areas with checkpoints and observation centres "ensured by the forces of the guarantors by consensus", but that "third-party" monitors could also be deployed.

But on Monday, Syrian Foreign Minister Waild Muallem rejected the idea of UN or international monitors.

"We do not accept a role for the United Nations or international forces to monitor the agreement," he said.

He added that there could be a role "as the Russian guarantor has said, for military police", but it was unclear if he was referring to Syrian or foreign units.

Russia meanwhile said on Monday that it had tabled a draft UN Security Council resolution backing the safe-zone deal.

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