The Ukrainian military command said the pro-Russian rebels had attacked 112 times since early Sunday, mostly in the bitterly contested Debaltseve area.
A Ukrainian officer said there was also fighting near Mariupol, a port city.
The rebels accused Ukrainian forces of shelling Donetsk airport.
Meanwhile, further EU sanctions against Russia have gone into effect.
The new sanctions list targets 19 officials - most of them in the pro-Russian separatist strongholds of Donetsk and Luhansk, but also two Russian deputy defence ministers and a Russian celebrity singer and MP, Iosif Kobzon.
Armed separatist groups are also targeted, including a Cossack formation.
Those listed are now subject to visa bans and asset freezes across the EU.
Russia is accused of fomenting the revolt in eastern Ukraine and giving the separatists reinforcements and heavy weapons.
Russia denies doing so, but admits that Russian "volunteers" are fighting there.
In the past 24 hours, five Ukrainian soldiers died in fighting at Shirokyne, near Mariupol, the Ukrainian military said.
Observers from the OSCE security body are to try again to reach the besieged Ukrainian town of Debaltseve.
They said they were denied access by the rebels on Sunday.
The rebels say they have the town encircled so it should be considered theirs.
On Monday, rebel commanders said there were no grounds yet to withdraw heavy weapons from the combat zone.
The withdrawal is supposed to start on Monday, under the Minsk agreement.
"Heavy weapons will be withdrawn if the Minsk accords are observed. Those conditions are not in place yet," said rebel defence spokesman Eduard Basurin.
Rebel "defence minister" Vladimir Kononov said:
"We will withdraw heavy weapons from the contact line if we get a definite sign that the Ukrainian side has started doing the same thing".
On the Ukrainian side, a military spokesman quoted by Reuters news agency said there would be no withdrawal of heavy weapons yet because the rebels were violating the ceasefire.
Elsewhere on the front line reports say the ceasefire has broadly been observed.
According to the Minsk agreement, reached last week, the ceasefire is only the first step.
It should be followed on day two by a withdrawal of heavy weapons - lasting two weeks - to create buffer zones 50-140km (30-85 miles) wide.
Analysts point out that previous ceasefires initially appeared to be holding but eventually failed, and say the next 48 hours are critical.
Officials say almost 5,500 people have been killed since the conflict erupted in eastern Ukraine in April, but the UN believes the actual death toll to be much higher.
An EU official said the latest sanctions were intended to punish the Russian-backed rebels for a rocket attack on Mariupol last month which killed more than 30 civilians.
"The sanctions were meant to come into force last week, but they were postponed because the EU didn't want to interfere with the Minsk talks. But they always intended to implement these sanctions, and today, they have," the official said.
The sanctions are intended to dissuade Russia from further action, the official added.
"The EU is ready to reverse them when Russia shows willingness to find a political solution. Minsk is a step in the right direction, but now the EU needs to see the ceasefire enter into force," he said.
Ukraine conflict: The human cost
- 5,486 people killed since conflict began in April 2014
- 12,972 wounded across eastern Ukraine
- 5.2 million people estimated to be living in conflict areas
- 978,482 internally displaced people within Ukraine, including 119,832 children
- United Nations report, 6 February