"The actions by the Russia-backed separatists in Debaltseve are a clear violation of the ceasefire," the EU's foreign affairs head Federica Mogherini said in a statement.
"The separatists must stop all military activities," Mogherini added, only moments after Ukrainian President Petro Poroshenko announced that beleaguered Kiev troops had withdrawn from the flashpoint town.
"Safe passage for all those who want to leave the area must also be ensured," Mogherini said.
Journalists and monitors from the Organisation for Security and Cooperation in Europe tasked with overseeing the ceasefire have been prevented by rebels from entering the town.
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"The EU calls 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," the statement said.
"The EU stands ready to take appropriate action in case the fighting and other negative developments in violation of the Minsk agreements continue."
The EU warned Russia last week it was prepared to impose more sanctions if the new Ukraine peace pact signed in the Belarusian capital last week was breached.