Tensions also rose around a new flashpoint -- the port city of Mariupol on the Azov Sea -- with Kiev accusing Russia of trying to wrest it away through the deployment of several tanks.
A bomb killed two people during a pro-government march in the east Ukraine city of Kharkiv on Sunday, officials said, as Kiev's army and rebels wrangled over a truce requiring them to pull back heavy weapons.
The Kharkiv blast tore through a "Dignity March" marking the one-year anniversary of the overthrow of the country's former pro-Kremlin president, one of several that took place across Ukraine.
Regional prosecutor Yuri Danilchenko described it as a "homemade bomb packed with shrapnel, put in a plastic bag and hidden in snow by the side of the road."
One of those killed was a police officer. Another 11 people were wounded.
An AFP journalist saw the two bodies lying on the ground covered with Ukrainian flags.
"I thought it was a stun grenade, but then I saw people fall down," an organiser of the march, Igor Rasokha, said.
Kharkiv is located more than 200 kilometres (120 miles) from Ukraine's frontline, which continues to be contested in several areas despite a UN-backed truce meant to come into effect a week ago.
US, EU eye more sanctions
Ukraine's military and the rebels sought to salvage parts of the truce Sunday, agreeing to pull back heavy weapons from the frontline and swapping prisoners overnight.
But even those steps were fraught.
Within hours, the insurgents said the weapons withdrawal would only begin on Tuesday, after a couple of days of "preparation". Kiev insisted that it was meant to start on Sunday with no delays.
And both sides said fighting continued near the port city of Mariupol, held by the army but becoming a new focus for fighting in the 10-month conflict that has killed more than 5,700 people.
Kiev said Russia had sent 20 tanks to near Mariupol. Defence spokesman Andriy Lysenko claimed there were "two tank attacks" reported early Sunday at the city, and ongoing fighting.
Further breaches of the already tattered ceasefire could bring "serious" additional sanctions on Russia "within days," the US has warned.
US Secretary of State John Kerry said on Saturday that "if this failure continues, make no mistake, there will be further consequences including consequences that will place added strains on Russia's already troubled economy".
EU president Donald Tusk, who participated in Kiev's "Dignity March", said he would "begin consultations on Monday to increase some of the measures in connection with the aggression" in Ukraine, the Interfax-Ukraine news agency reported.
The US, the EU and Ukraine all accuse Russia of being behind the separatist insurgency.
Russia denies the accusation, but has already been hit by successive rounds of Western sanctions that are savaging its economy, which is headed for recession because of a collapse in oil prices.
The worst breach of the ceasefire was a bloody offensive by the pro-Russian rebels on Debaltseve, a strategic transport hub between the separatist strongholds of Donetsk and Lugansk.
The rebels overran the town on Tuesday, sending 2,500 Ukrainian soldiers fleeing and taking more than 110 prisoner.
Some of those detained were among 139 Ukrainian soldiers swapped overnight for 52 rebel fighters in the frontline town of Zholobok.
A few of the soldiers struggled on wooden crutches across a war-torn landscape cratered and littered with twisted metal.
One freed insurgent, Roman Biarinov, vowed he would quickly return to the fight. "We have to defend this land. We are going to win. I don't know how, but we will win," he said.
The International Committee of the Red Cross said in a statement it delivered food, blankets and medical supplies to some 5,000 people who had been trapped in Debaltseve by the combat.
By Sergiy Bobok with Stephane Jourdain in Donetsk (AFP)