Mahmoud Abbas and Ehud Olmert have held their third meeting in the past few weeks.
"We consider it reassuring that high-level contacts are becoming regular. This provides prerequisites for restoring stable political dialogue between Israel and the Palestinian National Authority, as well as substantive Palestinian-Israeli negotiations on the basis of international law," the ministry said.
It said Russia supports the positive trend in Palestinian-Israeli relations, and will continue to facilitate the implementation of the Mecca inter-Palestinian accords.
Palestinian Islamist group Hamas visited Moscow in late February against the backdrop of a deadlock in peace talks with Israel and bloody inter-factional clashes in Palestinian lands, and in the wake of a series of international meetings on the Middle East conflict.
Russian Foreign Minister Lavrov said Russia backed the idea of establishing a national unity government for the PNA from the very beginning in May 2006, and that Russia has consistently supported steps to promote the process.
Hamas and the President Mahmoud Abbas-led Fatah movement agreed to form a power-sharing Cabinet in Mecca, ending weeks of bloody street clashes between their supporters.
Russia, a member of the Quartet that also comprises the United States, the UN and the EU, has tried to forge international support for the initiative and encouraged international donors to resume financial aid, suspended after Hamas radicals came to power in January 2006.
A Quartet meeting in Berlin February 21 and an earlier meeting in Washington failed to bring a coordinated approach to the problem and a decision to resume aid over the U.S. and other countries' doubts surrounding Hamas's refusal to recognize Israel and renounce violence.
