The German plan, backed by the EU, stipulates a non-violence agreement, confidence-building measures over the next year to lead to a determination of Abkhazia's status, and the return of Georgian refugees to Abkhazia.
"We agreed that work must be continued to convince, as soon as possible, the sides to begin direct talks," Lavrov said, adding that the sides must themselves find "common ground."
Abkhazia rejected the peace plan earlier on Friday, calling it "unacceptable." Georgia has given its overall backing for the plan.
German Foreign Minister Frank-Walter Steinmeier, rounding off a two-day visit to Georgia, Abkhazia, and Russia, admitted that the Georgian and Abkhazian positions were still far apart, adding however that this did not mean the peace process should be abandoned.
"I am glad we have seen the willingness of our partners to enter into talks that could resolve a range of issues," he said, noting that this would require many days and weeks of negotiations.
Lavrov and Steinmeier then left for a meeting with Russian President Dmitry Medvedev.
Before the meeting, Lavrov said the German plan for the resolution of the Georgian-Abkhazian conflict was a step in the right direction, but dismissed a proposed agreement on the return of Georgian refugees to Abkhazia as unrealistic.
Some 300,000 Georgians fled Abkhazia in 1991-93 amid accusations of ethnic cleansing. In mid-May, the UN General Assembly adopted a resolution acknowledging ethnic cleansing in Abkhazia and called for the return of Georgian refugees.
Abkhazia broke away from Georgia in the early 1990s following the collapse of the Soviet Union. Between 10,000 and 30,000 people were killed in the subsequent hostilities. The two sides signed a ceasefire in 1994 in Moscow.
