JERUSALEM, Dec 16 (Reuters) - The U.S. Middle East envoy held separate talks with Israeli and Palestinian leaders this week during his first trip to the region since the United States called off efforts to revive direct negotiations.

What happened to those negotiations, what has U.S. envoy George Mitchell said and done this week and what are the prospects of success for another round of indirect talks Washington now says it will pursue?

WHAT HAPPENED TO THE NEGOTIATIONS?

The Palestinians pulled out of the face-to-face talks with Israel at the end of September when it refused to extend a 10-month partial freeze on construction in settlements in the occupied West Bank.

They said any resumption of the talks, which had started only a few weeks earlier, depended on a full halt to Jewish settlement building in the West Bank and East Jerusalem.

That remains their position. The Palestinians say settlement construction is undermining any chance of establishing a viable Palestinian state alongside Israel.

The United States said last week it had called off efforts to persuade Israel to impose a settlement freeze, effectively declaring an end to its efforts to revive the direct talks.

The Obama administration and Israeli Prime Minister Benjamin Netanyahu had failed to reach agreement on security incentives that the Israeli leader sought in return for agreeing to extend the freeze.

WHAT IS HAPPENING NOW?

The United States says it will pursue indirect talks between the sides. Secretary of State Hillary Clinton said in a Dec. 10 speech the United States would not be a passive participant. We will push the parties to lay out their positions on the core issues, she said.

This week, Mitchell held talks with Netanyahu and Palestinian President Mahmoud Abbas. Netanyahu has stated his support for the new U.S. initiative.

In the days ahead, our discussion with both sides will be substantive two-way conversations, with an eye toward making real progress in the next few months on the key questions of an eventual framework agreement, Mitchell said.

The Palestinians say they have already presented Mitchell with their positions on the main issues of the conflict, such as borders, security arrangements and the future of Jerusalem.

Nabil Abu Rdainah, the spokesman for Abbas, said on Tuesday the Palestinians had asked Mitchell to come back to them with Israel's ideas on what the borders of a future Palestinian state would look like. Mitchell said he would be back soon.

WHAT ARE THE CHANCES OF SUCCESS?

Analysts were already sceptical about the chances of success before the peace talks were derailed in September. The U.S. failure to revive face-to-face talks has made them even more so.

The Palestinians, dismayed at the shift in the U.S. approach, have expressed serious doubt about whether a new round of indirect talks will make any headway at all. They say they are concerned about the agenda of such talks, arguing that Israel will avoid discussion of the main issues.

Netanyahu says he is prepared to tackle core issues and is committed to achieving a framework agreement with the Palestinians that will ensure both peace and security.

Arab officials who convened a meeting on the peace process in Cairo on Wednesday expressed pessimism. The American mediator has nothing new to offer, Qatari Prime Minister Sheikh Hamad bin Jassim al-Thani said after the meeting.

Israeli-Palestinian differences over a main focus for indirect talks are also weighing on chances for success. Palestinians want to know what the borders of a future state will look like.

Netanyahu has put the emphasis elsewhere, on protecting national security and demanding Palestinians recognise Israel as a Jewish state, a call they have rejected. (Writing by Tom Perry; editing by Mark Heinrich)