"When Israel does that, the Palestinian people will make their position clear."
Earlier, Lavrov, called for international support for the power-sharing arrangement that Hamas and Fatah signed in Mecca earlier in the month, and for the lifting of the international financial aid blockade against the Palestinian Authority.
However, the Quartet of Middle East peace brokers, which includes Russia, has said recognising Israel is a condition for resuming aid.
A spokeswoman for Ehud Olmert, the Israeli prime minister, criticised Lavrov's remarks, saying: "This is not the international community's stand and it's not the Quartet's stand."
Russia, which has been seeking a greater role in the Middle East, has been more positive about the unity government plan than Washington and the EU.
Meshaal, who was part of the Hamas delegation that visited Moscow in March 2006, thanked Russia for "taking brave steps to host us".
"We highly value Russia's stance ... in support of the national accord between the Palestinians and lifting of the blockade," he said at the start of his talks with Lavrov.
"The land of Israel belongs to both Jews and Palestinians - as long as there are people who reject this fact, the conflict will never be solved"
Iskander, Boston, US
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It was not immediately clear if Russia's expression of support for the power-sharing agreement meant it was stepping back from the Quartet demands.
Russia favours the agreement between Hamas and the Fatah group to share power because it shows "wisdom, reason and responsibility before the Palestinian people", Lavrov said.
"We are pushing for all members of the international community to support this process and make it irreversible, including efforts to lift the blockade."
Crucial foreign aid
Millions of dollars in foreign aid were cut off after Hamas gained control of the cabinet and the legislature when it won elections in January 2006.
The European Union, US and others consider Hamas a "terrorist" group.
Since the power-sharing deal worked out this month in Saudi Arabia, however, there has appeared to be a softening in the stance of some EU countries towards Hamas.
Jacques Chirac, the French president, has said he would ask the EU at a summit in March to support plans for a unity government.