Both sides in the conflict have begun withdrawing their heavy weaponry from the front line of the conflict, in line with a peace deal agreed to in Minsk, Belarus, two weeks ago.
There has also been a reduction in the fighting between the two sides, although some artillery fire can still be heard. But the ceasefire remains fragile.
A spokesman for Ukrainian President Petro Poroshenko cited him as saying on Twitter: "We starting withdrawing only some of the heavy weaponry. Ukrainian military are ready to return the equipment to the front line any time."
The leader of the self-proclaimed Donetsk People's Republic, Alexander Zacharchenko, said separatist forces there had withdrawn 90% of their heavy weapons.
But he also warned that they reserved the right to return the weapons to the front line if authorities in Kiev did not keep their end of the bargain.
A CNN team on the ground saw a small convoy of artillery, flying the yellow-and-blue flag of Ukraine, heading south out of the conflict zone Thursday. The separatists began the withdrawal of heavy weapons a couple of days earlier.
Under the terms of the Minsk agreement, the two sides have until Monday to complete the withdrawal and create a buffer zone of at least 50 kilometers (31 miles) for heavy weapons. The Organization for Cooperation and Security in Europe is tasked with monitoring the ceasefire and the withdrawal.
Ukraine's National Defense and Security Council said Friday that three Ukrainian troops had been killed and seven injured in the past 24 hours in continued clashes.
Russia warns about gas supply
Meanwhile, Russian Energy Minister Alexander Novak warned that Russian energy giant Gazprom could cut the supply of natural gas to its neighbor in the coming days if payment is not received.
Russia's Tass state news agency said that Gazprom confirmed receiving $15 million Friday in prepayment from Ukraine. But that is enough to pay for only a day's supply of natural gas, the news agency said.
A meeting between the European Union, Russia and Ukraine is due to take place in Brussels, Belgium, on Monday to discuss gas supply to Ukraine.
Russia has used gas as a weapon before, cutting off supplies to Ukraine three times in the past decade. A new dispute could affect the rest of Europe. About a third of the European Union's natural gas comes from Russia
, and 15% flows through Ukraine.
However, now that the worst of winter is over, the threat of a halt in the supply of gas is less alarming than it was for Ukraine and for the rest of Europe.
In any case, Kiev has reserve gas supplies that could be used if the supply from Russia were stopped. Europe also has the option of reverse supply -- sending gas back through pipelines into Ukraine.
The latest disagreement comes against the backdrop of an EU investigation into Gazprom
, which is due to report soon. Europe has accused Gazprom of using its dominant position to manipulate prices and hinder the free flow of gas across the continent.
Lavrov: Need to consolidate weapons withdrawal
The developing situation in eastern Ukraine was the focus of an emergency U.N. Security Council meeting in New York on Friday.
The chief monitor for the OSCE mission to Ukraine, Ertugrul Apakan, reported some progress in implementing the Minsk agreement as he briefed the council, but said much remained to be done.
"For the past days, combat operations have been significantly reduced across the conflict zone, although some violence has still occurred around Donetsk airport, as well as close to the town of Mariupol," he said.
"As to the withdrawal of heavy weapons, yesterday our monitors began observing the movement of heavy weapons away from the line of contact on several instances."
However, the OSCE needs more information in order to monitor their withdrawal effectively, he said, including what heavy weapons each side has, where they are now and where they will be taken.
There are currently 451 civilian monitors in Ukraine, he said, of whom more than 300 are in the contested Donetsk and Luhansk regions.
The mission will need more technological resources, such as drones, in order to cover a huge area of operations extending about 50,000 square kilometers (19,300 square miles), including large stretches of the Russia-Ukraine border, he said. More hubs may also have to be set up for OSCE patrols.
Ertugrul also highlighted the plight of more than 1 million people forced from their homes within Ukraine, "some of them living in desperate circumstances."
Russian Foreign Minister Sergey Lavrov, speaking Friday at his ministry's Diplomatic Academy, said: "Impartial observers, including the Organization for Co-operation and Security in Europe, have registered a significant reduction in the exchange of fire, so the ceasefire is nonetheless yielding a result."
But he stressed that although some progress has been seen in the withdrawal of heavy weapons, "it is important to consolidate it."
He also warned that Ukraine must keep its nonaligned status "in order to keep the stability in Europe."
Russia is unhappy about what it sees as NATO
's expansion toward its western border. Ukraine is not a NATO member, but Baltic nations bordering Russia belong to the alliance and Georgia also hopes to join.
Ukraine and the West accuse Russia of arming and training the separatists, as well as sending Russian troops over the border to fight with them. Russia denies the claims.