RAMALLAH (Ma'an) -- President Mahmoud Abbas said Wednesday a key component of peace and stability in the Middle East was an agreement between the Israelis and Palestinians.

Such a scenario requires a deal between the two sides, and after that ties between Israel and the rest of the Arab and Islamic world, Abbas was quoted as saying by Palestinian Authority media.

At a joint news conference with the president of the European Council in Brussels, Abbas said that "yesterday we raised the Palestinian flag at UNESCO, and I hope in the future we will raise it at the UN."

Standing alongside Herman Van Rompuy, the EC president, Abbas said he hoped Palestine's admission to the UN would come as the result of active support from the European Union, Wafa reported.

"We appreciate this long term support, and hope it will continue until the completion of the construction of the Palestinian institutions, in preparation for the declaration of the Palestinian state," he added.

On the topic of internal politics, Abbas said, "We are very interested in reaching a Palestinian reconciliation between Hamas and the Palestine Liberation Organization to bring back national unity."

Rompuy, meanwhile, said "I emphasize that the European Union remains committed to the two-state solution ... We will continue to expect that any future Palestinian government adhere to the principles to which Abbas has committed."

President Abbas "informed me of the current developments in the Palestinian request for membership in the United Nations," he added hoping the Arab spring would "have a positive effect on the Middle East peace process."

Also Wednesday, representatives of the international peacemaking Quartet were holding separate talks with Israeli and Palestinian officials, diplomats said, with no breakthrough in sight.

The envoys, representing the United Nations, Russia, the United States and the European Union, met the Palestinian team headed by Mohammed Shtayeh at the UN headquarters in East Jerusalem, they said.

They were expected to hold talks with the Israelis at the same place in the early afternoon.

Quartet envoys last met with Israeli and Palestinian negotiators exactly a month ago, but made no progress, saying only they had "continued to encourage the parties to resume direct bilateral negotiations without delay or preconditions."

Direct talks have been on hold for over a year, grinding to a halt shortly after they restarted in September 2010 after Israel refused to extend a partial freeze on illegal settlement construction

Last week, the US State Department said it was sending its Middle East peace envoy David Hale to Jerusalem as part of its "efforts to get the two parties to put forward concrete proposals and to agree to come back to the table together."

The Quartet laid out a proposal in September aimed at reaching a peace agreement in a year.

But there has been no visible sign of progress, with the PLO demanding that Israel halt building Jewish-only settlements on Palestinian land before the talks can be resumed.

On Monday, Israel approved construction of 40 homes in a new settler enclave near the West Bank town of Bethlehem, effectively expanding a large settlement bloc there.