But the wide gaps between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas left it uncertain if or when the meeting will take place, and raised doubts about whether they would make any progress if they do get together.
In another twist, an Israeli TV station reported that a document discovered by two Israeli researchers indicated that Abbas had worked for the Soviet intelligence agency, the KGB, while living in Syria in the early 1980s.
The professors said they were coming forward with the information to discredit Moscow as an honest broker in peace talks.
After years of taking a back seat to the US in Mideast diplomacy, Russia has increasingly sought to take a leadership role in the region. It has developed close ties with Iran and sent fighter jets to Syria to back President Bashar Assad in his war against rebel groups.
In Washington, a spokesman said the US State Department is following the Russian efforts closely and would "be supportive" of any kind of effort to bring the parties together.
Today's announcement in Moscow indicates that Russia is pushing forward with its attempt to become a peace broker after a setback earlier in the week. On Tuesday, Abbas said that a meeting scheduled in Moscow this week had been delayed at Israel's request.
While bringing the men together would represent an accomplishment for Moscow, a diplomatic breakthrough seems unlikely.
Abbas and Israeli Prime Minister Benjamin Netanyahu remain far apart on key issues, and their differences have prevented meaningful talks since Netanyahu took office in 2009.
The last round of peace talks broke down two and a half years ago, with no progress reported during months of US-brokered negotiations.
In Moscow, Russian Foreign Ministry spokeswoman Maria Zakharova said Abbas and Netanyahu had accepted an invitation to meet in the Russian capital, but a date has not been set yet.
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