UNITED NATIONS, Dec 14 (Reuters) - Prospects for a two-state solution in the Middle East could start to evaporate next year unless there is progress in U.S.-mediated indirect Israeli-Palestinian talks, a U.N. envoy said on Tuesday.

Washington is pinning its hopes on shuttle diplomacy after Israel refused to extend a 10-month freeze on housing starts in settlements on the West Bank -- a Palestinian condition for direct talks. U.S. envoy George Mitchell launched the first round this week.

Robert Serry, U.N. special coordinator for the Middle East peace process, told Reuters in an interview that the end of direct talks, which began in September but lasted only a few weeks, was a serious setback in the quest for a peace deal.

He said it is essential that the Israelis and Palestinians make serious proposals on core issues, such as borders and the status of Jerusalem, and that Israel ease restrictions on the occupied West Bank.

The very opportunity for a two-state solution may be fading next year if everything fails. That is something I hope the parties are realizing, Serry said, stressing the need for very proactive mediation led by the United States.

A two-state solution would see Israel living alongside an independent Palestinian state. In September, Israeli and Palestinian leaders pledged to try to achieve that within a year and the Palestinian Authority promised to be ready for statehood by then.

CREDIBILITY AT STAKE

Serry was speaking after delivering a monthly briefing to the U.N. Security Council, where he called for a substantive third party role in mediation, including by the Quartet -- the United States, Russia, the United Nations and European Union.

He said Quartet principals -- expected to group U.S. Secretary of State Hillary Clinton, Russian Foreign Minister Sergei Lavrov, U.N. Secretary-General Ban Ki-moon and EU foreign policy chief Catherine Ashton -- would meet early in 2011.

In the year ahead, the credibility of the political process and of its sponsors, including the Quartet, will ... be at stake, he told the council.

Speaking to Reuters, Serry played down the likelihood that the Palestinian Authority would seek to have the U.N. General Assembly make a proclamation of Palestinian statehood, as some Palestinians have suggested. Such a proclamation would have no legal force, diplomats say.

Any attempt to have the 15-nation Security Council issue such a declaration is bound to be vetoed by the United States but the 192-nation assembly, where there is no veto, has a pro-Palestinian majority.

Going ... to the U.N. and asking for statehood in a unilateral fashion, I think (the Palestinians) realize is not going to bring the goal of a two-state solution any nearer, Serry said.

They know that the only way to the endgame is a negotiated endgame. I think the leadership is still convinced about that.

Asked about the view of some analysts that a one-state solution, grouping Jews and Arabs, now looked inevitable, Serry said: Everybody should understand that a one-state solution is simply no solution. It simply means continued conflict for decades. (Writing by Patrick Worsnip; editing by John O'Callaghan)