Mousa Abu Marzouk, a Hamas politburo member, met Russian Deputy Foreign Minister Mikhail Bogdanov in Moscow.
"We discussed issues related to Palestinian national unity and the creation of a government that should govern the Gaza Strip after the war," Marzouk was quoted as saying by RIA.
Marzouk said that Hamas had asked Russia to encourage Abbas, who is attending the BRICS summit in Kazan, to start negotiations about a unity government, RIA reported.
Abbas is head of the Palestinian Authority (PA), the governing body of the occupied Palestinian territories.
The PA was set up three decades ago under the interim peace agreement known as the Oslo Accords and exercises limited governance over parts of the occupied West Bank, which Palestinians want as the core of a future independent state.
The PA, controlled by Abbas' Fatah political faction, has long had a strained relationship with Hamas, the Islamist movement that runs Gaza, and the two factions fought a brief war before Fatah was expelled from the territory in 2007.
Israeli Prime Minister Benjamin Netanyahu has expressed strong opposition to the PA being involved in running Gaza.
