* Thousands evacuate Ghouta towns to north, more prepare to go
* No sign of deal yet over last remaining rebel pocket
* U.N. says people who fled undergo screening process (Adds state TV interviews with men who accepted reconciliation deal)
BEIRUT/AMMAN, March 27 (Reuters) - Thousands of people left eastern Ghouta for Syrian rebel territory near the Turkish border on Tuesday, the third large group to leave under a deal brokered by Russia to surrender the enclave near Damascus to the Syrian government.
Government forces were also mobilising around Douma, the last rebel-held town in eastern Ghouta, a war monitor reported, piling pressure on the insurgents holed up inside to cut a similar deal.
The Jaish al-Islam group, which has so far refused to leave Ghouta, said Russia had yet to give an answer to proposals that involve its fighters and civilians staying in Douma, adding that a meeting was expected on Wednesday.
Rebels have been leaving other parts of Ghouta in batches with their families, accepting safe passage to the Idlib region in the northwest after they were beaten into retreat in a fierce assault by the Russia-backed Syrian army.
It marks the biggest defeat for the rebellion against President Bashar al-Assad since insurgents were driven from eastern Aleppo in 2016, underscoring his unassailable military position after seven years of conflict.
Some 7,000 people - most of them fighters and their families - left on 100 buses in the early hours of the morning, the monitor, the Syrian Observatory for Human Rights, said. More buses drove into eastern Ghouta ahead of a further evacuation.
"We faced two choices: go to Idlib or make peace with the regime," said Sakhr Yousef, a 24-year-old fighter with the Failaq al-Rahman faction, as he was preparing to leave eastern Ghouta with his wife and four young siblings.
"Making peace with the regime is very difficult, making peace with those who bombed us with criminal Russia," he added in a voice message to Reuters, referring to Assad's main backer in the conflict.
The Syrian military split eastern Ghouta into three separate zones during its assault that began on Feb. 18 and has killed more than 1,600 people, according to the Observatory.
The rebels being evacuated on Tuesday are leaving from a pocket encompassing the towns of Arbin, Ain Tarma and Zamalka that was controlled by Failaq al-Rahman rebels.
The last remaining insurgent-held area in Ghouta is the town of Douma. The Islamist group that controls it, Jaish al-Islam, is in talks with Russia that have yet to yield a result.
"We have presented our decision to stay. This is not only a decision by Jaish al-Islam, but by all the revolutionary institutions and figures in Douma," said Hamza Birqdar, the group's military spokesman.
The United Nations said it is concerned for 70,000-78,000 people it said were trapped in Douma and is ready to provide aid if the government lets it in.
"The United Nations and its partners are ready to proceed to Douma with food for up to 16,500 people, as well as health, nutrition and water, sanitation and hygiene supplies. But facilitation letters have to be signed by the Government of Syria," Mark Lowcock, U.N. Under-Secretary-General for Humanitarian Affairs, said in a statement.
DISPLACED PEOPLE SUBJECTED TO "SCREENING PROCESS"
Backed by Russia and Iran, the government has repeatedly forced rebels to surrender areas and withdraw to Idlib, where the UN now describes situation as "catastrophic". The opposition has called this a policy of "demographic change" aimed at forcing dissidents out of Syria's main cities.
State television, broadcasting from the outskirts of Arbin, showed buses moving along a dusty road through a wasteland of heavily damaged buildings.
A correspondent with Hezbollah's al-Manar TV said it could take four to five days to evacuate the tens of thousands of people who had agreed to leave Arbin, Ain Tarma and Zamalka.
Hezbollah, a heavily armed Lebanese group backed by Iran, has fought on Assad's side during the war.
The Russian news agency TASS said 13,190 rebels had left eastern Ghouta in the last three days.
Tens of thousands of people have also fled eastern Ghouta this month into areas controlled by the Syrian government.
The U.N. Office for the Coordination of Humanitarian Affairs (OCHA) said more than 80,000 people had left formerly besieged parts of eastern Ghouta as control shifted since March 9.
The displaced "have to proceed to collective shelters and are not permitted to leave, until they have undergone a screening process and are able to prove a sponsor", OCHA said in a situation report.
The International Committee of the Red Cross (ICRC) warned on Tuesday that the displaced people were at risk from communicable diseases and said procedures for people to leave the shelters "should be accelerated".
"Many children who are already extremely weak are being exposed to further health hazards like diarrhoea, lice and skin diseases. We have seen many children who had to walk many kilometres barefoot or in completely worn-out shoes," the ICRC said in a statement.
Syrian state TV said the army freed 28 people who had been held captive by militants in Arbin. The Observatory said their release was part of the deal agreed by rebels.
Syrian state television Ikhbariya spoke to some of what it said were 315 men associated with rebel groups who had chosen not to go to Idlib but to reconcile with the government.
The interviewer asked the men, sitting on government buses in formerly rebel-held Harasta, to describe conditions under the rebels.
One man said rebels had imprisoned him for 44 days for "talking about them". Several others described the situation as "bad, very bad".
One said they had been made to dig tunnels for the rebels. Another said the rebels had large food stores. "We were surprised when we saw the rice, sugar, tea, bulgur wheat. While we were in need of rice."
The government says the offensive is securing Damascus from insurgent mortar fire that regularly used to hit the capital including its Old City.
In addition to their foothold in the northwest, anti-Assad rebels still hold a chunk of territory along the southern frontier with Jordan and Israel, and enclaves near Damascus, Homs and Hama. (Additional reporting Katya Golubkova and Lisa Barrington Writing by Tom Perry Editing by Mark Heinrich and Hugh Lawson)