The United States, Russia, the European Union and the United Nations will focus on peace talks underway between the Israelis and Palestinians, including a ceasefire agreement between Tel Aviv and the radical Islamic group Hamas, which came into force on Thursday.
The ceasefire deal brokered by Egypt states that Israel will gradually lift economic sanctions against the Palestinian enclave, Hamas will stop rocket attacks, and the two will continue talks on the release of a kidnapped Israeli soldier held in Gaza for two years.
Israeli troops, meanwhile, killed two Palestinians, including an Islamic Jihad leader, in the West Bank on Tuesday. The truce only applies to Gaza.
Peace talks that Israel and Syria have been holding since May after an eight-year gap will also be on the agenda of the Quartet.
Lebanon has rejected Israel's proposal to resume peace talks, saying the Jewish state should first withdraw from what it considers to be occupied Lebanese territory.
Berlin is also due to host a separate conference on security and justice in the Palestinian Territories on Tuesday.
The Russian Foreign Ministry said Moscow would urge support for efforts to promote the unity of Palestinian factions at the talks. Hamas seized the Gaza Strip over a year ago from Palestinian President Mahmoud Abbas' Fatah movement.