MOSCOW, June 2 (RIA Novosti) - A meeting of foreign ministers from the Middle East Quartet could be held in June, Russian Foreign Minister Sergei Lavrov said on Tuesday.

Russia, the United States, the European Union and the United Nations, comprise the Middle East Quartet of intermediaries which are seeking ways to settle the Israeli-Palestinian conflict.

"Israel and Russia actively support efforts currently under way to create the conditions [to resume the negotiation process], including the work of the Quartet, which plans its latest ministerial-level meeting this month," Lavrov said following talks in Moscow with his Israeli counterpart, Avigdor Lieberman.

Talks between Israel and the Palestinian Authority, launched after a peace conference hosted by then U.S. president George Bush in November 2007, stalled following an Israeli offensive on Gaza in December which left 1,300 Palestinians dead and 5,000 others injured.

The tragic events in Gaza pushed the conflicting Palestinian groups to seek dialogue in order to form a single government.

The Russian minister said both Russia and Israel are in support of Egypt's efforts aimed at restoring Palestinian unity based on the Palestine Liberation Organization and called on Hamas and Fatah to do the same.

"We are also sending signals both to Hamas and [Palestinian leader Mahmoud] Abbas on the need to seriously cooperate with Egypt's efforts," Lavrov said.

The Hamas and Fatah movements, the largest political organizations, split in June 2007 when Hamas took control of the Gaza Strip and pushed the Fatah movement out of the enclave of 1.5 million. Hamas has since remained in power in Gaza, independent of the officially recognized government of Fatah in the West Bank, which is headed by Palestinian President Mahmoud Abbas.

Lieberman said, however, that Israel is ready to discuss all issues concerning a peaceful settlement with the Palestinians except for construction of Jewish settlements in the West Bank.

"Settlers and settlement activities are not an obstruction to a peace agreement or a peaceful resolution," he said.

Last month U.S. President Barack Obama, historically Tel Aviv's strongest ally, urged Israeli Prime Minister Benjamin Netanyahu to put an end to the construction of Jewish settlements in the West Bank.

Netanyahu, a hard liner, has refused to commit Israel to ending its expansion policy, and has shown a greater reluctance to consider a "two-state solution" than his predecessor, Ehud Olmert.