Lavrov, who has participated at the Munich Security Conference, said on Saturday that a ceasefire had been brokered at a conference between Ukraine, Russia, Germany and France.
The Russian foreign minister described the ceasefire as a positive step but noted that there was an absence of "major progress" in talks.
Leader of east Ukraine's Russia-backed forces Alexander Zakharchenko has threatened to drive out Ukrainian troops from Donetsk and Luhansk provinces if political measures to "free the occupied territories" do not bear fruit.
Moscow said Zakharchenko's statement defied the 2015 Minsk agreement between Ukraine and pro-Russia forces, but added that it came in reaction to tensions provoked by Kiev's actions.
On Friday, Ukraine's President Petro Poroshenko warned Western governments during the Munich Security Conference in Germany against any "appeasement" of Moscow.
Poroshenko insisted that cutting a bilateral deal with Russia on his country would only lead to further deterioration of armed clashes in eastern Ukraine.
Poroshenko also stated that the administration of new US President Donald Trump had a "historic chance" to halt "Russian expansionism" in Ukraine.
The development comes as some European nations remain concerned over Washington's position toward Moscow under Trump amid persisting reports of a more cooperative relationship.
Nearly 10,000 people have perished in eastern Ukraine since April 2014 during fighting between government forces and pro-Russia fighters. Fighting escalated for several days earlier this month, the worst outbreak of armed clashes since a 2015 truce deal.