Fighting around Ukraine's port city of Mariupol comes as Russian President Vladimir Putin says he thinks the prospect of all-out war between Russia and Ukraine is unlikely.
Asked in an interview with Russian state television if he thought the current situation could lead to war, Putin said: "I think that such an apocalyptic scenario is unlikely and I hope that it will never happen."
"If the Minsk accords (agreeing a ceasefire) are complied with, then I am sure that the situation will gradually get back to normal."
He added: "No one needs a conflict, moreover an armed one, on the periphery of Europe."
A meeting of the foreign ministers of Ukraine, Russia, Germany and France was scheduled to take place in Paris on Tuesday to discuss the truce's implementation.
However, a source in the Ukrainian foreign ministry raised doubt, saying Ukrainian Foreign Minister Pavlo Klimkin "intends to go to the meeting tomorrow (Tuesday), but the situation might change".
Continued hostilities have meant a pull-back of heavy weapons could not go ahead as agreed, Ukrainian officials said.
"As Ukrainian positions are still being fired upon, there can be no talk yet of a withdrawal of arms," military spokesman Vladyslav Seleznyov wrote in a statement on Facebook on Monday.
Tensions were also high following a bomb blast on Sunday in the normally peaceful eastern city of Kharkiv. In their latest toll, authorities said that three people had died in the "terrorist" attack.
Ukraine's currency, the hryvnia, plummeted about 10 per cent on Monday because of the instability.
The West has warned of additional sanctions on Russia should the shaky truce deteriorate further, especially after rebels captured the strategic town of Debaltseve last week in defiance of the ceasefire slated to start on February 15.
The Organisation for Security and Cooperation in Europe, tasked with monitoring the truce, "concludes that the ceasefire is not holding in critical, strategic points", including near Mariupol and in Debaltseve, the deputy head of the OSCE mission, Alexander Hug, told France 24 television.
A Ukrainian military commander, Colonel Valentyn Fedichev, said the number of attacks had generally decreased across the conflict zone, but troop positions were still fired upon 27 times since Sunday. 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.
Other defence officials said the rebels fired mortars into Shyrokine, which neighbours Mariupol, in an apparent attempt to provoke troops into firing back in violation of the ceasefire.
Kiev has alleged Russia sent 20 tanks towards Mariupol, a port city of half a million residents on the Azov Sea coast, and that two tank attacks occurred there on Sunday.
If Mariupol were to fall to the pro-Russian rebels, it would remove a key obstacle to creating a separatist land corridor stretching from Russia's border with Ukraine to Crimea.
"An advance on Mariupol would clearly be in breach of the agreements" underpinning the truce brokered by Berlin and Paris, German Foreign Minister Frank-Walter Steinmeier said in an interview with his country's Bild newspaper.
German government spokesman Steffen Seibert said: "It fills us with concern that there is still no comprehensive truce."
Up to now, the main compliance with the Minsk agreement has been a prisoner swap conducted on Saturday in which nearly 200 captured fighters from both sides were traded.
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