Tensions were also high following a bomb blast yesterday in the normally peaceful eastern city of Kharkiv. In their latest toll, authorities said that three people had died in the "terrorist" attack.
The West has warned of additional sanctions on Russia if the shaky truce should deteriorate further, especially after rebels last week took the strategic town of Debaltseve in defiance of the ceasefire meant to start February 15.
A withdrawal of heavy weapons from the frontline a key step of the truce has still not gone ahead despite both sides on Sunday agreeing to start the process.
The rebels, meanwhile, have sent mixed messages, alternately saying that they have pulled back some weapons or that they will start on tomorrow.
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A Ukrainian military commander, Colonel Valentyn Fedichev, said Monday that, while generally across the conflict zone "the intensity of the number of attacks has decreased", troop positions were still fired on 27 times since yesterday.
Two Ukrainian soldiers were killed and 10 wounded, he said.
Insurgent fighters "have not halted attempts to assault our positions in the town of Shyrokine and the Mariupol area," Fedichev said.