Ukrainian President Petro Poroshenko has said government forces were completing a "planned and organized" withdrawal from the eastern town of Debaltseve, which has been at the epicenter of fighting between Ukrainian troops and pro-Russian militants in recent weeks.
"As of now, we can say that 80 percent of our units have left," Poroshenko said, adding that two more columns were expected to pull out.
Hostilities have continued in Debaltseve, a key transportation hub linking the rebel-held cities of Donetsk and Luhansk, despite a cease-fire brokered by European leaders last week and supposed to have taken effect on February 15.
Mykola Kolesnyk, the leader of a pro-government paramilitary unit, confirmed that Ukrainian forces were pulling out but said not all were withdrawing.
"We are talking only about units which are surrounded in populated areas in and around the town," he told the 112 television channel.
Semen Semenchenko, a Ukrainian lawmaker who heads another pro-government battalion, said on Facebook that the rebels were trying to block Ukrainian forces from leaving Debaltseve.
Eyewitnesses were quoted as saying dozens of tanks and columns of Ukrainian troops were retreating from the city.
Russia's state-owned Channel One television channel showed the separatists raising their flag over a high-rise building in Debaltseve.
Separatist leaders said they were also pulling back their fighters and artillery from some parts of the frontline.
They claimed hundreds of Ukrainian troops had surrendered, while Russian state-run television showed images of several dozen Ukrainian troops being escorted along a village road by the rebels.
Ukrainian authorities admitted that soldiers had been taken prisoner in Debaltseve but gave no details of how many were captured.
NATO Secretary-General Jens Stoltenberg said that he was "deeply concerned" by the situation around the besieged town and that "the refusal of the separatists to respect the cease-fire" threatened the agreement.
He urged Russia to end its support for the separatists and withdraw its forces and military equipment from eastern Ukraine.
In Berlin, Chancellor Angela Merkel's spokesman Steffen Seibert said Germany "strongly condemns the military actions of the separatists in Debaltseve," describing them as a "major violation" of the latest truce deal reached and a "heavy strain" on hopes for peace.
French government spokesman Stephane Le Foll said the cease-fire deal "was not dead" and that his country would do "everything to keep the agreement alive"
The leaders of Russia, Ukraine, Germany, and France are expected to hold a telephone conference later on February 18 to discuss the situation in Ukraine.
The developments come after Russian President Vladimir Putin urged Ukrainian troops in Debaltseve to surrender.
On February 18 in Moscow, Russian Foreign Minister Sergei Lavrov said the truce was in place in almost all frontline areas except Debaltseve.
He also said the situation in Debaltseve should not be used to disrupt the peace process in Ukraine.
Earlier, U.S. Vice President Joe Biden accused Russia of violating the Minsk accord.
Meanwhile, the European Union's foreign affairs chief, Federica Mogherini, condemned the rebel offensive against the town as a "clear violation" of the cease-fire.
"Safe passage for all those who want to leave the area must also be ensured," the statement said.
It also called for "immediate access of the OSCE Special Monitoring Mission to assume its monitoring and verification functions in and around Debaltseve and to any other site the Mission needs to go."
Militants themselves accuse Ukrainian forces of breaching the cease-fire and argue that the truce does not apply to Debaltseve, which they say is inside rebel-held territory and thus not part of the truce agreement.
The rebels have barred observers from the Organization for Security and Cooperation in Europe (OSCE), the group responsible for monitoring the cease-fire, from entering the Debaltseve area.
WATCH: Behind Rebel Lines In Debaltseve
The conflict in eastern Ukraine has already killed more than 5,600 people and displaced more than a million others, according to a United Nations estimate.
It has also left the country's industrial heartland in ruins.
Also on February 18, rebels in the Donetsk region said they have brought "criminal charges" against Ukraine's top leaders.
The "prosecution service" of the separatist leadership in Donetsk said Poroshenko, Prime Minister Arseniy Yatsenyuk, and National Security and Defense Council Secretary Oleksandr Turchynov have been "charged with planning, preparations and waging of aggression and war " in Ukraine's east.
The developments come as Canada imposed additional sanctions on Moscow and its sympathizers over the Ukraine conflict.
The new economic sanctions announced on February 17 target 37 Russian and Ukrainian individuals as well as 17 Russian and Ukrainian entities, including Russian's oil giant Rosneft.
Canadian Prime Minister Stephen Harper said his government "remains steadfast in its commitment to stand with the people of Ukraine in the face of the Putin regime's ongoing military aggression."
Russia's Foreign Ministry said it "reserves the right to react accordingly" to the Canadian sanctions.
With reporting by Reuters, AP, AFP, and Interfax