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(CNN) Evacuations began for thousands of civilians and rebels from Syria's eastern Aleppo on Thursday, but for many, fleeing their homes means leaving one war zone for another.

Most of the civilians will be taken to rebel-controlled area in the neighboring province of Idlib, one of the few remaining footholds rebel groups still have in the country -- and most likely the regime's next target for recapture. Rebel fighters were also being allowed to move there.

Approximately 3,000 people and more than 40 wounded were brought out of eastern Aleppo during the first two evacuations on Thursday, the head of the International Committee of the Red Cross in Syria, Marianne Gasser, said in a statement.

Evacuations are expected to continue throughout the night and into Friday, according to Syrian state TV.

But while the world's attention has been focused on Aleppo, Idlib has been pounded with regime airstrikes and dozens of deaths have been reported in recent weeks.

Latest developments

Syrian President Bashar al-Assad congratulates Syrians on "liberation" of Aleppo

But CNN sources on the ground say rebels are still in control of some of the city

Evacuations have begun, with many civilians bound for Idlib province

Thousands of others remain in rebel-held Aleppo

Convoy carrying injured civilians came under fire, leaving one dead and four injured

Grim choice for families

The grim choice of whether to stay or go is a difficult one for Abdulkafi al-Hamdo, an English teacher and activist with a 9-month-old daughter.

"I'm thinking of leaving. I'm thinking of what would happen if we didn't leave," he said.

If he does leave, he said he hopes his daughter would "come back to Aleppo as a young girl who knows the meaning of freedom."

Busses carrying injured people leave eastern Aleppo.

Haid Haid's sister is stuck in East Aleppo. He's a Chatham House Syrian columnist and researcher in London and told CNN his sister had tried to leave Thursday, but there were too many people.

"She will try again tomorrow," he said. "Only a few buses are provided. It's a slow process and if it stays the same it will take days" until Eastern Aleppo is empty.

The evacuations began with a convoy of 20 buses and 13 ambulances after previous attempts failed on Wednesday. A new ceasefire was agreed overnight after predominantly Shia Iran and the militias it backs pushed for the evacuation of two Shia enclaves, Al-Foua and Kefreia in rebel-held Idlib province.

Twenty-nine buses started evacuations in those two cities Thursday, according to Syrian State TV.

Some of the people are injured and suffering medical problems, including anemia and malnutrition, said Dr. Zaher Sahloul, a senior adviser to the Syrian American Medical Society.

"You have patients who are very traumatized psychologically because of what they've witnessed of extreme violence, destruction and the killing of their family member."

With colder temperatures setting in, people need not just medical care, but shelter too, he said.

Will evacuations continue peacefully?

Turkish President Recep Tayyip Erdogan said Thursday the number of people remaining in Eastern Aleppo "is not that small. It is big. I hope the process will not be interrupted," according to Turkish state news agency Anadolu.

Turkish Prime Minister Binali Yildirim asked his Russian counterpart, Dmitry Medvedev, to make sure that evacuation operations will continue safely and without harm to civilians, Anadolu reported.

U.S Secretary of State John Kerry said all parties should work toward a sustainable ceasefire in the Syrian conflict, but warned the evacuation of Aleppo must remain peaceful.

"What has happened already in Aleppo is unconscionable," Kerry said. "But there remains tens of thousands of lives that are now concentrated into a very small area of Aleppo, and the last thing anybody wants to see -- and the world will be watching -- is that that small area turns into another Srebrenica."

If Aleppo falls completely and people are "slaughtered," Kerry said it will be hard to bring people together for any possible peace talks.

Meanwhile, Syrian President Bashar al-Assad congratulated the Syrian people on the "liberation" of Aleppo on Thursday, adding that "history is being written by every Syrian citizen."

He spoke in a new video posted on his office's YouTube channel. His office did not provide details on where he recorded the statement.

But CNN sources on the ground say that parts of eastern Aleppo are still under rebel control.

The Syrian regime has for days been on the brink of taking the whole city of Aleppo, having made sweeping gains in just over two weeks since its forces, backed by airstrikes, entered the enclave by ground. Rebels ruled eastern Aleppo for four years before the regime offensive.

Aleppo torn down

As night fell over the troubled city, the evacuations continued.

They are beginning with the injured, the vulnerable, and rebel fighters and their families, said Jan Egeland, special adviser to the U.N. special envoy for Syria, earlier Thursday.

Most would be taken to Idlib, he said, while others who choose to can go to Turkey.

The UN was not part of the evacuation agreements but has been given access to monitor the process, along with the International Committee of the Red Cross.

"It took 4,000 years, hundreds of generations, to build Aleppo. One generation managed to tear it down in four years," Egeland said.

"Aleppo, for 3,000 years, gave to world civilization and world civilization was not there to assist the people of Aleppo when they needed us the most."

Sniper fire hits convoy

Earlier, one person was killed and four others injured when a truck carrying volunteer rescuers from the White Helmets group was shot at. It was attempting to clear a path for ambulances, according to Dr. Hamza al-Khateab, the manager of Aleppo's al-Quds hospital. The ambulances also came under fire.

Desperate civilians wait for evacuation from Aleppo on Thursday.

But the operation ground to a halt when a truck clearing a route for ambulances came under fire. Among those injured was Bebars Meshaal -- chief officer of the White Helmets, also known as the self-styled Syrian Civil Defense -- who lost his kidney in the attack, al-Khateab said.

The White Helmets and the Aleppo Media Center (AMC) activist group claim regime snipers were behind the attack.

CNN is unable to independently verify the details.

Meshaal is now in a stable condition, al-Khateab said.

'History will not forgive'

If the regime does take control of the key city it would mark a turning point in the brutal five-year civil war that has killed hundreds of thousands of people. It would put the regime back in charge of all five major cities, making a political opposition far less likely.

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But the leader of the opposition Aleppo City Council, Brita Hagi Hasan, was still hopeful that despite the rebels losing territory, a political opposition with international backing would be possible.

"We need urgent cohesion to force the regime and Iranian militia present on the ground to respect the ceasefire, and we need the organization of safe exit of the civilians. And then we need, based on the evidence of the (UN) Security Council, to remove the legitimacy of this regime," said Hasan in Brussels after meeting with European Council President Donald Tusk.

Iranian militia groups, as well as others loyal to Assad, are fighting alongside regime forces.

The UN Security Council has been widely criticized as toothless, having failed for years to find a political solution to the Syria crisis that broke out in 2011. Russia has used its veto power as a permanent member several times to shoot down resolutions, as has China.

"All the war crimes that have been committed, the crimes against humanity, are crimes that have killed the international law. And despite this, it seems that this regime retains legitimacy in the eyes of a lot of countries," Hasan said.

"History will not forgive -- history is registering the international silence in front of these crimes against humanity."