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(CNN) The latest evacuations from eastern Aleppo resumed Wednesday after a brief delay, according to Syrian state television.

No reason was given for the delay. The International Red Cross said snow has been falling and many are struggling to keep warm.

According to Syrian state TV, a number of buses with armed people and their families were leaving the Al-Sokkari area in eastern Aleppo and heading to Al-Rashdin in western Aleppo.

We took this video near the front line in #Aleppo this morning. With snow falling, it's freezing and many have little means to keep warm. pic.twitter.com/Oa0hECDuYs

It said 20 buses departed from eastern Aleppo on Wednesday, while 1,500 civilians are expected to be evacuated from Kafraya and Foua villages in mainly rebel-held Idlib province simultaneously.

The Red Cross confirmed that all hospital patients have been evacuated in eastern Aleppo .

The last hospital in Eastern #Aleppo is now empty. All patients have been evacuated, along with other people in need of urgent medical care. pic.twitter.com/QyAq8IpkZc

Israel offers help

On Tuesday, Israeli Prime minister Benjamin Netanyahu said Israel wanted to help treat those who had been wounded in Aleppo.

Israel has treated thousands of Syrians over the past couple of years at the Ziv Medical Center in the north of the country.

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"We see the tragedy, the terrible suffering of civilians," Netanyahu said.

"I've asked the Foreign Ministry to seek ways to expand our medical assistance to the civilian casualties of the Syrian tragedy, specifically in Aleppo where we're prepared to take in wounded women and children and also men if they're not combatants.

"We'd like to do that, bring them to Israel, take care of them in our hospitals, as we've done with thousands of Syrian civilians.

"We're looking into the ways of doing this, but it's being explored as we speak."

Tens of thousands evacuated from Aleppo

On Tuesday, state-run TV station Al-Ikhbariya reported the Syrian army had used loudspeakers to urge remaining rebels to leave the area, warning it intended to enter the enclave to "remove remnants of terrorism."

More than 37,000 people have already been evacuated from Aleppo, Turkish Foreign Minister Mevlut Cavusoglu tweeted. The remainder, he hoped, would be out of the besieged city by Wednesday.

The International Committee of the Red Cross has put the number of evacuees since last Thursday at 25,000 and said the operation is "still ongoing."

A further 750 people have so far been evacuated from the largely Shiite villages of Fuaa and Kafraya in Idlib province as part of the same deal, the ICRC said.

A shaky ceasefire, a careful evacuation

Photos: Battle for Aleppo Civilians wait to be bussed out of besieged areas of eastern Aleppo, Syria, as evacuations continue on Monday, December 19. A people-swap deal struck between rebels and Syrian government forces was set to begin over the weekend, but evacuations were temporarily put on hold after a number of buses were set on fire. Hide Caption 1 of 35 Photos: Battle for Aleppo Syrian pro-government forces wave to evacuees from the villages of Foua and Kefraya on December 19. While people were being bused out of Aleppo, safe passage was also given to people in areas held or besieged by rebels, the Aleppo Media Center activist group said. Hide Caption 2 of 35 Photos: Battle for Aleppo Militants burned at least five buses assigned to evacuate people in Aleppo on Sunday, December 18. Aleppo has been held by rebels for the past four years, but it is now almost entirely under government control. Hide Caption 3 of 35 Photos: Battle for Aleppo Buses drive through the Syrian government-controlled crossing of Ramoussa, on the southern outskirts of Aleppo, on December 18. Hide Caption 4 of 35 Photos: Battle for Aleppo Russian soldiers and Syrian pro-government forces look on as civilians and rebel fighters are evacuated from Aleppo on Friday, December 16. Evacuations began a day earlier under a new ceasefire between rebels and pro-government forces. Hide Caption 5 of 35 Photos: Battle for Aleppo Pro-government forces guard a convoy of buses and ambulances during the evacuation operation on December 16. Hide Caption 6 of 35 Photos: Battle for Aleppo Civilians arrive in the opposition-controlled Khan al-Aassal region, to the west of Aleppo, on Thursday, December 15. Most of the civilians from Aleppo will be taken to a rebel-controlled area in the neighboring province of Idlib. Hide Caption 7 of 35 Photos: Battle for Aleppo A wounded boy sits inside an ambulance during the evacuations on December 15. Hide Caption 8 of 35 Photos: Battle for Aleppo Staff members of the Syrian Red Crescent wait near ambulances as the evacuation operation gets underway on December 15. Hide Caption 9 of 35 Photos: Battle for Aleppo Buses line up to transport people away from eastern Aleppo on December 15. Hide Caption 10 of 35 Photos: Battle for Aleppo A woman leads family members toward the evacuation buses on December 15. Hide Caption 11 of 35 Photos: Battle for Aleppo A woman in a wheelchair waits to board a bus during evacuations on December 15. Hide Caption 12 of 35 Photos: Battle for Aleppo A member of the civil defense carries a wounded boy out of a hospital in eastern Aleppo on December 15. Hide Caption 13 of 35 Photos: Battle for Aleppo Pro-government forces advance in Aleppo on Wednesday, December 14. Hide Caption 14 of 35 Photos: Battle for Aleppo A wounded woman is helped into the bed of a truck on December 14. Hide Caption 15 of 35 Photos: Battle for Aleppo Buses wait to evacuate people in Aleppo on December 14. Hide Caption 16 of 35 Photos: Battle for Aleppo Pro-government forces advance on December 14. Hide Caption 17 of 35 Photos: Battle for Aleppo Pro-government forces walk in the ancient Umayyad Mosque after capturing the area on Tuesday, December 13. Hide Caption 18 of 35 Photos: Battle for Aleppo Syrians depart a rebel-controlled area of Aleppo on December 13. Hide Caption 19 of 35 Photos: Battle for Aleppo Syrian residents, fleeing violence in the Bustan al-Qasr neighborhood, arrive in Aleppo's Fardos neighborhood on December 13. Hide Caption 20 of 35 Photos: Battle for Aleppo A Syrian child cooks in the street in a rebel-held area of Aleppo on December 13. Hide Caption 21 of 35 Photos: Battle for Aleppo Syrian civilians take food from a storage room that was formerly held by the opposition forces in eastern Aleppo's al-Kalasseh neighborhood on December 13. Hide Caption 22 of 35 Photos: Battle for Aleppo Pro-government fighters wave from a truck as they pass civilians fleeing the Bustan al-Qasr neighborhood on December 13. Hide Caption 23 of 35 Photos: Battle for Aleppo A woman reacts as she evacuates the Bustan al-Qasr neighborhood with her two children on December 13. Hide Caption 24 of 35 Photos: Battle for Aleppo Syrians celebrate in a government-held district of Aleppo on Monday, December 12. Hide Caption 25 of 35 Photos: Battle for Aleppo Pro-government forces patrol the al-Saleheen neighborhood in eastern Aleppo on December 12. Hide Caption 26 of 35 Photos: Battle for Aleppo Rebels in southeastern Aleppo target government forces with anti-aircraft weaponry on December 12. Hide Caption 27 of 35 Photos: Battle for Aleppo Civilians flee the Sukkari neighborhood in southeastern Aleppo on December 12. Hide Caption 28 of 35 Photos: Battle for Aleppo Pro-government forces patrol Aleppo's Sheikh Saeed district on December 12 after it was recaptured from rebel forces. Hide Caption 29 of 35 Photos: Battle for Aleppo In this handout photo from the International Committee for the Red Cross, women displaced from eastern Aleppo gather at a shelter in the village of Jibreen, south of Aleppo, on December 12. Hide Caption 30 of 35 Photos: Battle for Aleppo Smoke rises from the Bustan al-Qasr neighborhood on December 12. Hide Caption 31 of 35 Photos: Battle for Aleppo Civilians from eastern Aleppo stream into a government checkpoint at the al-Hawoz street roundabout on Saturday, December 10. Hide Caption 32 of 35 Photos: Battle for Aleppo Rebel fighters take aim at pro-government positions in Aleppo on Friday, December 9. Hide Caption 33 of 35 Photos: Battle for Aleppo Syrian rebels walk down a street in eastern Aleppo on December 9. Hide Caption 34 of 35 Photos: Battle for Aleppo Clouds of smoke billow from eastern Aleppo's al-Shaar neighborhood on Monday, December 5. Hide Caption 35 of 35

By the end of last week, the Syrian army had made enough progress in its offensive for President Bashar al-Assad to refer to the progress made as the "liberation" of Aleppo.

"History is being written by every Syrian citizen," Assad said.

After reclaiming some rebel territory, Syrian officials and rebel leaders agreed to a ceasefire designed to grant civilians safe passage out of the city. Humanitarian workers initially helped about 9,000 people leave Aleppo behind.

This past Friday, the evacuation stopped, placing the fragile accord in doubt, after Iranian militias targeted the road that leads into besieged areas of eastern Aleppo with 23-millimeter gunfire, according to the Aleppo Media Center, or AMC, activist group.

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Tens of thousands of refugees were left in limbo, many of the them forced to sleep outdoors, or in bombed-out buildings, as temperatures plunged below zero.

Both sides struck another agreement the following day to provide safe passage to those loyal to Assad's regime, including Iranian militia groups, from areas held or besieged by rebels, AMC said. It was a new demand in exchange for the evacuation of civilians, rebels and others loyal to the opposition from eastern Aleppo.

On Monday, the United Nations Security Council voted unanimously to redeploy staff to Aleppo to monitor and report on the evacuation of civilians.

Leaving or left behind in Aleppo?

It's not clear how many civilians are left in Aleppo, but the evacuations could wrap up this week.

Of those leaving, some will head to Idlib province. But for many, being taken to Idlib is trading one war zone for another. Idlib is widely expected to be the regime's next target, and the evacuations are effectively moving rebels to one containable zone.

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Turkey is building a new refugee camp for the evacuees from eastern Aleppo. The camp is in the countryside of Idlib and will be able to host 50,000 people when finished.

Turkey, whose once-icy ties with Russia have thawed in recent months, found itself pulled further into the conflict this week as a police officer assassinated the Russian ambassador in Ankara while shouting: "Do not forget Aleppo!"

Russia and Turkey have agreed to work together on an investigation -- and have vowed to not let the shooting derail progress made toward the end of the war in Syria.