JERUSALEM, Oct 11 (Reuters) - Prime Minister Benjamin Netanyahu offered the Palestinians a trade off on Monday to revive peace talks they quit -- a new freeze on building in settlements if they recognise Israel as a Jewish state.

The Palestinians immediately rejected making any such declaration, which they have long opposed.

The impasse deepened doubts over the chances of resuming U.S.-brokered negotiations that stalled last month after Israel refused to extend a 10-month moratorium on housing starts in Jewish settlements in the occupied West Bank.

If the Palestinian leadership will say unequivocally to its people that it recognises Israel as the homeland of the Jewish people, I will be ready to convene my government and request a further suspension, Netanyahu told parliament.

This is not a condition but a trust-building step, which would create wide-ranging trust among the Israeli people, who have lost trust in the Palestinian will for peace over the last 10 years, he said.

The direct talks were kicked off in Washington on Sept. 2, but there were only three face-to-face sessions before the building freeze expired.

Netanyahu made his move on Monday just three days after the Palestinians and Arab powers had given the United States a month to persuade Israel to declare a new moratorium.

All settlement is illegitimate, it must be frozen for a return to negotiations, said Nabil Abu Rdainah, spokesman for Palestinian President Mahmoud Abbas.

The issue of the Jewishness of the state has nothing to do with the matter, he told Reuters, adding that the Palestinians had already recognised Israel and that this should suffice.

REFUGEES

The Palestinian leadership argues that recognition of Israel as a Jewish state would compromise the rights of Arab citizens of Israel who make up 20 percent of the population.

Such a move, Palestinian officials say, 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.

George Giacaman, a political scientist at Birzeit University near the West Bank city of Ramallah called Netanyahu's proposal a non-starter.

I think the Americans will try a last ditch effort to find a formula acceptable to both sides, he said.

If this is the last word, the political process will stall and the Palestinian leadership will be forced to look at alternatives, Giacaman said.

In his policy speech opening the winter session of parliament, Netanyahu also cited the need for strong measures to ensure Israel's security under any peace deal.

He said Israel was weighing U.S. proposals, including ideas touching on security, to salvage the negotiations, whose collapse would be a sharp diplomatic failure for U.S. President Barack Obama.

A senior Israeli official has said Washington is seeking a two-month extension of the settlement-building moratorium to give more time for direct diplomacy.

Palestinians view settlements, on land Israel occupied in a 1967 war, as an obstacle to the establishment of a viable and contiguous state.