"We have reached agreement under which, within 48 hours, we will call on (Palestinian leader) Mahmud Abbas to launch consultations on the creation of a government" of national unity, senior Fatah official Azzam al-Ahmad told a press conference, speaking in Arabic.
Ater the government is formed, the Palestinians would set up a national council, which would include Palestinians in exile, and hold elections.
"Today the conditions for (such an initiative) are better than ever," said Ahmad.
The non-official talks in Moscow began on Sunday under Russian auspices with the goal of restoring "the unity of the Palestinian people." Representatives came from Fatah, Hamas, Islamic Jihad and other factions.
Abbas's secular party Fatah and the Islamist Hamas have been at loggerheads since the latter seized Gaza in a near civil war in 2007.
Last year the Palestinian government postponed the first municipal polls in the occupied West Bank and Gaza Strip in 10 years after the high court ruled they should be held only in the Fatah-run West Bank.
The last time the Palestinians staged elections in which both Hamas and Fatah took part was in 2006.
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The Palestinian representatives also met on Monday with Russian Foreign Minister Sergei Lavrov, and asked him to dissuade incoming US president Donald Trump from carrying out a campaign pledge to move the US embassy in Israel from Tel Aviv to Jerusalem.
Israel captured east Jerusalem during the 1967 war and later annexed it -- in a move not recognised by the international community -- declaring all of the city its unified capital.
"We sensed understanding on the part of Mr. Lavrov," said Ahmad.
Ahmad and Moussa Abu Marzouk of Hamas spoke derisively of the Quartet -- the United States, Russia, the EU and UN -- in its years-long effort to end the Israeli-Palestinian conflict.
"The Quartet's work completely failed. It was unable to advance the decisions taken by the international community, including (UN) resolutions," said Ahmad.
"It is imperative to find a new working mechanism for the Israeli-Palestinian conflict," he said.
Abu Marzouk, a senior Hamas official, said he no longer wanted to work with the Quartet but instead with countries and organisations on an individual basis.
"Russia can play a substantial role" in the region, he said.