"We will expect the new Israeli government to be committed to the agreements which were concluded earlier...in Annapolis," Lavrov said.
Earlier on Wednesday, the centrist Kadima party led by Foreign Minister Tzipi Livni and the opposition right-wing Likud party headed by former prime minister Benjamin Netanyahu both claimed victory in Israel's early parliamentary polls.
Lavrov said Israel's three-week military operation in Gaza that started on December 27 and left more than 1,300 Palestinians dead should not discourage all sides from seeking a peaceful solution to the Palestinian issue.
"It is also necessary to consider resuming the peace process which has suffered a severe blow. We should not lose heart," the Russian foreign minister said.
Lavrov said Russia's and the EU's positions on the Middle East almost coincided.
"We have almost identical positions on Middle East affairs," Lavrov told reporters following talks with top EU foreign policy officials in Moscow.
The EU was represented by Czech Foreign Minister Karel Schwarzenberg, whose country holds the European Union's rotating presidency, Carl Bildt, his counterpart from Sweden, which takes over the presidency on June 1, EU foreign policy chief Javier Solana and EU External Relations Commissioner Benita Ferrero-Waldner.
According to Lavrov, the talks focused on European security, conflict settlement in the Middle East, anti-piracy operations and Russia's participation in international peacekeeping operations.
Russia's top diplomat also said the timing of a Moscow conference on the Middle East would be announced soon.
"We will soon announce the timeframe for holding a Moscow conference [on the Middle East]," Lavrov said.
He added that Russia expected the conference to build on earlier international agreements on the problem, and that it would "continue what was started in Annapolis."
Talks between Israel and the Palestinian Authority, launched by U.S. President George Bush in November 2007 at a conference in Annapolis, Maryland, have been stalled by an outbreak of violence in the Middle East, as well as long-standing disputes over the construction of Jewish settlements and the future status of Jerusalem.
