(Adds Quartet statement and Moussa comment)

By Matt Spetalnick and Haitham Haddadin

UNITED NATIONS, Sept 26 (Reuters) - Palestinian President Mahmoud Abbas pledged on Friday to pursue peace efforts with Israeli Prime Minister Ehud Olmert's successor but warned of a new cycle of violence if the fragile peace process collapsed.

Abbas painted a cautious and at times bleak picture of Middle East peace efforts during a visit to the United Nations, casting further doubt on U.S. President George W. Bush's target of securing a peace deal before he leaves office in January.

Speaking at the Security Council, Abbas and other Arab leaders denounced Israeli settlement expansion, saying it was jeopardizing talks relaunched last November at a conference in Annapolis, Maryland, hosted by Bush.

Arab League Secretary-General Amr Moussa said Israeli settlements in the occupied West Bank made the prospects for a two-state solution "very difficult, if not impossible."

Israel's U.N. envoy, Gabriela Shalev, accused Arab delegations of using the issue to "bash" Israel unfairly, saying they were dodging their responsibility to condemn Hamas, which advocates the destruction of the Jewish state.

Despite increasing obstacles, U.S. Secretary of State Condoleezza Rice told Reuters "I think it's possible" to reach a deal by year-end that would include agreement on creation of a Palestinian state.

Meeting on the sidelines of the General Assembly, the "Quartet" of Middle East mediators urged "every effort to conclude an agreement before the end of 2008."

But signaling it may be hedging its bets, the group -- made up of the United States, Russia, the European Union and United Nations -- also said it favors holding a new international meeting on Israeli-Palestinian peace in Moscow next spring.

Talks have been complicated by political instability in Israel. Olmert resigned this week in the face of corruption allegations and is staying on in a caretaker capacity while Foreign Minister Tzipi Livni tries to form a new coalition.

"I will pursue negotiations with Mr. Olmert and I will never cease to negotiate even with his successor," Abbas said.

"DEADLY CYCLE"

But Abbas said that unless Israel halts expansion of settlements, "it would be futile to dream of the peace that we all hope for. Because if we fail, if we do not attain peace, then the alternative poses a serious threat.

"The alternative will plunge the entire region into the deadly cycle of violence once again. I don't even wish to imagine what that might lead us to," he added.

In his speech to the General Assembly, Abbas -- who governs only in the West Bank while Hamas Islamists control the Gaza Strip -- stopped short of reiterating the hope that a deal with Israel could be reached this year.

"Israel is prepared, if the conditions are ripe, to make painful concessions in the pursuit of peace," Shalev said.

Symbolic of that view, she said, was Israeli President Shimon Peres' meeting with Abbas shortly before the Council meeting, which was called at the behest of Arab countries.

The Quartet later issued a statement reiterating its call for Israel to freeze all settlement activity, which it said was having a "damaging impact on the negotiating environment."

It also condemned Palestinian attacks on Israelis, including rocket fire from Gaza, and "stressed the need for further Palestinian efforts to fight terrorism."

Shalev denied the settlements were "an obstacle to peace." Israel has insisted it has the right to build in large enclaves it intends to keep under any future peace deal.

Talks between the sides have yielded little amid flare-ups of violence in and around Gaza. Israel criticizes the Palestinian leadership for failing to rein in militants. (Editing by Xavier Briand)

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