JERUSALEM, Oct 12 (Reuters) - Prime Minister Benjamin Netanyahu threw a new twist into efforts to rescue Middle East talks by conditioning renewal of a partial settlement building freeze on Palestinian recognition of Israel as a Jewish state.

Palestinians, who have long rejected making any such declaration, immediately rebuffed the proposal announced on Monday and said they were sticking by their demand for a new construction moratorium before more peace talks can take place.

Here is a look at some of the problems and issues facing the U.S.-brokered peace process.

WHAT IS THE STATUS OF THE TALKS?

The Israeli and Palestinian leaders were expected to meet every two weeks for direct talks. The last such encounter was on Sept. 15 and no new date for a meeting has been fixed. The Palestinian leadership says direct talks will not resume unless Israel halts building settlements on occupied land. Prior to his proposed trade-off on Monday, Netanyahu had refused to extend a 10-month partial freeze on housing starts in settlements in the occupied West Bank. The moratorium expired on Sept. 26 and the Palestinians said at an Arab League meeting last week that they would give the United States one month to persuade Israel to halt building in settlements.

CAN THE IMPASSE BE BROKEN?

Faced with Palestinian rejection of his offer, Netanyahu said that he is still considering ideas put forward by the United States to keep the talks alive. Israeli officials say Washington has proposed a 60-day settlement construction freeze in return for U.S. security guarantees and increased military aid to Israel, incentives that appeared aimed at helping Netanyahu sell another moratorium to pro-settler parties in his governing coalition. Netanyahu's linkage of a freeze to Palestinian recognition of a Jewish state adds a new element to the diplomatic equation and seemed likely to complicate Washington's efforts to get peace talks under way again.

WHY DO THE PALESTINIANS INSIST ON THE FREEZE CONTINUING?

The Palestinians say the construction work undermines the very notion of a peace deal, arguing that every house built on the West Bank for Jewish families takes land away that they will need to create a viable state. Netanyahu argues that no previous Israeli leadership has been forced to halt building while peace talks were under way. The Palestinians say the building is now so extensive, the situation has become critical. The United States and European Union have both called for a settlement freeze, but they have yet to find a way of getting Netanyahu to budge.

WHY DO PALESTINIANS OBJECT TO RECOGNISING A JEWISH STATE?

The Palestinian leadership says this would compromise the rights of Arab citizens of Israel who make up 20 percent of the population. It says such a declaration also would effectively forgo the right of return of Palestinian refugees who fled or were forced from their homes in Arab-Israeli wars to return to territory that is now Israel.

WHAT HAPPENS NEXT?

If both sides continue to stick to their demands, the United States could try to switch back to indirect talks, but they have yielded almost nothing in previous months. Some Israeli commentators have said that Netanyahu's Jewish state demand was designed to appease his pro-settler coalition partners while he negotiates a solution to the impasse with the United States. In this case, he would ask the U.S. to sweeten its security guarantees and military aid package in exchange for renewing the settlement freeze. Other commentators said Netanyahu's focus on the Jewish state issue was proof that he was more concerned with the survival of his coalition than the peace talks and was interested only in shifting the blame to the Palestinians if they continued to reject his offer and U.S. efforts to revive the negotiations fail.

WHO WILL LOSE OUT IF THE TALKS COLLAPSE?

U.S. President Barack Obama's administration will look weak for launching talks that collapsed almost immediately. Questions will be asked of why it kicked off the negotiations on Sept. 2 without first resolving the obvious problem of a settlement freeze that was slated to expire only three weeks later.

The Palestinian Authority will look to maintain the status quo in the West Bank and few locals believe, despite further building in Israeli settlements, that there will be a repeat of the generalised uprising seen in 2000 following the collapse of Camp David peace talks. Netanyahu will have shored up his domestic position, but he risks alienating Obama.