But Russian President Vladimir Putin effectively withdrew from the Minsk agreement last week by signing an executive order recognizing travel documents issued by separatist authorities in the region.
Critics fear that recognizing the pro-Russian governments in eastern Ukraine is a step toward Putin's government declaring the disputed regions to be independent states.
But Putin spokesman Dmitry Peskov said that Russia is recognizing the travel documents "for humanitarian reasons."
"This law does not violate international law in any way," Peskov said. "For humanitarian reasons, it was necessary to do it and recognize these documents. Imagine, the situation only happened because of the official blockade of Kiev, hundreds of thousands (of people) do not have the opportunity to apply for passports, renew their passports, driving licenses, etc."
By "blockade," Peskov was referring to the claim that the Ukrainian capital was making life in the east difficult by not letting people apply for passports and pensions.
Ceasefire violations in eastern Ukraine have been significantly reduced since the new truce took effect at 12 a.m. local time Monday, but "ingredients" for a "further flare-up" remain, said Alexander Hug, chief monitor of the Organization for Security and Cooperation in Europe Special Monitoring Mission to Ukraine.
"Since midnight, we have seen them significantly reduced, and we have only seen up until now small arms fire in the Donetsk region, that is promising," Hug said by phone from Kiev.
"However, heavy weapons remain on both sides of the contact area where they shouldn't be, and positions of the Ukrainian armed forces and the formations on the other side are far too close to one another -- ingredients of further flare-up."
Ukrainian military spokesman Col. Oleksandr Motuzyanyk said, "The intensity of fire was 10 times less, but there were no calm places at the front line."
On Monday afternoon, he said there had been 24 ceasefire violations in the Donetsk region, including 12 with heavy weapons.
Ukrainian Secretary of National Security and Defense Oleksandr Turchynov said Putin's order was the death knell for the Minsk agreement, the framework for peace in the region since pro-Russian militants occupied areas of eastern Ukraine in 2014.
"By signing this decree, Putin legally recognized quasi-terrorist groups that have this as a fig leaf covering the Russian occupation of Donbass," he said.
The German government slammed Putin's move.
"Recognition of identity documents from separatist-held areas by #Russia is (a) clear violation of spirit and objective of #Minsk," the German Foreign Ministry tweeted.
Eastern Ukraine has seen a spike in violence in recent months between Russian-backed separatists and Ukrainian armed forces.
Russian Foreign Minister Sergey Lavrov said it was a positive move that the foreign ministers "agreed once again for the state of a ceasefire on February 20." He said the deal also includes the start of the withdrawal of heavy arms in eastern Ukraine.
OSCE Secretary-General Lamberto Zannier said that Putin's executive order would hurt the chances of the ceasefire to take hold.
It called for the "bilateral cessation of the use of all weapons," and the decentralization of power in the region "with respect to the temporary status of local self-government in certain areas of the Donetsk and the Lugansk regions."
At the time, Ukrainian Prime Minister Arseniy Yatsenyuk spoke with guarded optimism.
"We had just two options: bad, and worse," he said. "So we decided at this particular period of time to get the bad option. Probably this option will save the lives of Ukrainian soldiers, and I hope this option will save lives of Ukrainian civilians, of innocent people, who are under a constant shelling of Russian-led terrorists."
"It's better to have this new deal rather than not to have (it)," he said. "But we do not trust any words or any papers. We are to trust only actions and deeds."
Speaking at the Munich Security Conference in Germany on Saturday, Vice President Mike Pence told world leaders that the United States will stand firm against Moscow -- while also seeking avenues for cooperation.
"Know this -- the United States will continue to hold Russia accountable, even as we search for new common ground, which as you know, President Trump believes can be found," Pence said.
Outspoken Russian lawmaker Alexey Pushkov interpreted Putin's executive order as a response to the tough words that Pence and US Defense Secretary James Mattis have had for Russia in recent days.
"With the recognition of passports to Donetsk and Luhansk Peoples Republics, Moscow lets everybody know that pressure on the Ukrainian question won't give any results," Pushkov tweeted.
Euan McKirdy wrote from Hong Kong, and Emma Burrows reported from Moscow. CNN's Holly Yan, Radina Gigova, Victoria Butenko, Sebastian Shukla, Nick Paton Walsh and Kevin Liptak contributed to this report.
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Eastern Ukraine ceasefire begins -- but will it hold? - CNN.com