Pro-Russian separatists say they now control at least 80 percent of Debaltseve in eastern Ukraine. Fierce fighting has continued in the strategic city, despite a ceasefire deal signed just days ago.
Separatist commanders in Debaltseve said on Tuesday there were only a few residential areas left to seize before the whole city was under rebel control.
"In a few days, maybe even today, I hope that Debaltseve will be fully cleaned up," rebel defense minister Vladimir Kononov said on Russian state television.
He urged Ukrainian troops to retreat, saying their only choice was "to leave behind weaponry, lay down arms and surrender."
The fighting in Debaltseve hit the city's streets for the first time on Tuesday, with pro-Russian separatists aiming to wrest the center of the city - a key transportation hub which connects the rebel strongholds of Luhansk and Donetsk - from Ukrainian government forces. By the afternoon, the rebels claimed to have the upper hand.
Rebel spokesman Eduard Basurin was quoted by German news agency DPA as saying that 80 percent of Debaltseve was under rebel control, and that dozens of Ukrainian soldiers had been taken prisoner during a sweep of the city.
"We are scouring the city for more soldiers," Basurin said.
In a statement, Ukraine's defense ministry denied the city had been lost to the separatists, but acknowledged a group of soldiers had been taken prisoner, and that "part of the town has been seized by...bandits" backed by artillery and armored vehicles.
Ceasefire fails to take hold
The surge in fighting in Debaltseve has met with alarm from the European Union, with officials calling on the warring sides to observe the ceasefire and pull back heavy weapons from the front line.
"We remain concerned about the continued fighting in and around Debaltseve," European Commission spokeswoman Catherine Ray told a press briefing on Tuesday. "We recall once again the need for all sides to adhere strictly to the provisions of the package signed last week and carry out its measures without delay."
Under the truce deal, which was negotiated by Russia, France, Germany and Ukraine in Minsk last week and went into force on Sunday, both sides were supposed to begin withdrawing heavy weapons on Tuesday.
Ukrainian military spokesman Andriy Lysenko said his country would begin the withdrawal "as soon as the ceasefire is applied."
As fighting raged in Debaltseve, rebel spokesman Bassurin was quoted on Tuesday as saying the truce had held in the area around the rebel stronghold of Donetsk since Monday evening. He said the separatists were willing to take the "initiative" and pull back on some parts of the front line there.
Igor Plotnitsky, the leader of the self-proclaimed Luhansk People's Republic, northeast of Debaltseve, told the Russian news agency TASS that "our tanks, our artillery were pulling back." The claims have not been independently verified.
The separatists were expected to discuss the withdrawal of weaponry later Tuesday with representatives of Ukraine, Russia and the Organization for Security and Cooperation in Europe.
According to the United Nations, the conflict in eastern Ukraine has killed more than 5,600 people and displaced more than one million.
nm/msh (Reuters, AFP, AP, dpa)