Foreign Minister Frank-Walter Steinmeier and his French counterpart Laurent Fabius had invited the pair to the German capital.
So far, attempts to bring a halt to the bitter fighting between the Kiev-based government of the former Soviet republic and pro-Russian separatists had proved fruitless.
But Steinmeier said on Wednesday night that the talks had made "serious progress".
"If we manage to do this, then we can really call it a de-escalation of the conflict", Lavrov said.
While no "breakthrough" had been achived, it was "one step closer to the summit in Astana", Steinmeier added.
A new date for the planned four-way summit in the Kazakh capital has yet to be found after the mid-January deadline was passed.
Diplomats hope that bringing together Russian President Vladimir Putin, Ukrainian President Petro Poroschenko, Chancellor Angela Merkel and French President François Hollande will bring them closer to a solution.
The Berlin talks have focused on how a ceasefire agreed in Belarusian capital Minsk in September should be implemented on the ground, as recent weeks have seen renewed fighting between government and rebel forces.
But they were overshadowed by a war of words at the UN Security Council in New York between the American and Russian Ambassadors, with the US accusing Russia of trying to build a protective barrier of "frozen conflicts" around its borders.
US Ambassador Samantha Power called a peace proposal from Moscow "a Russian occupation plan".
Meanwhile, Russian representative Vitali Tschurkin accused the US of playing a "destructive role" in the Ukraine conflict, saying that the renewed violence flared up at the same time as a visit to Kiev by top US general in Europe Ben Hodges.
"Wherever Washington casts its eye, at Iraq, Libya, Syria or Ukraine, everywhere there is destabilisation, crisis and blood", he said.
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