* Obama has little to show for months of effort in Mideast
* Israeli-Palestinian peace competes with other priorities
* Effort will continue, if only to prove U.S. commitment
By Alistair Lyon, Special Correspondent
BEIRUT, Oct 23 U.S. President Barack Obama's high-priority Middle East peace drive has run into predictable quicksands, even as other foreign policy challenges in Iran, Afghanistan, Pakistan and beyond clamour for his attention.
Israel has rebuffed Obama's request for a complete freeze on settlement construction, while Arab states, whose own peace offer has gathered dust since 2002, have brushed off his calls for goodwill gestures toward the Jewish state.
Sceptics point to a rightwing Israeli cabinet more focused on threats from Iran, Hezbollah and Hamas than on making peace with Palestinians mired in rivalry between Islamist militants ruling the Gaza Strip and their Fatah foes in the West Bank.
Secretary of State Hillary Clinton gave her boss a status report on Thursday which appeared to confirm widespread doubts inside and outside the region that progress is possible.[nN2251043]
"This represents a clear failure by a president who tried to bring about change and, a year on, admits he has failed," Yossi Beilin, an Israeli architect of the 1993 Oslo Accords with the Palestinians, told Israel's army radio on Friday.
Washington still hopes to relaunch peace talks that stalled in December if it can forge a deal on their terms of reference.
But Israeli officials say the Americans envisage talks based on decades-old U.N. Security Council resolutions that each side interprets differently -- an unpromising recipe for success.
Israeli Prime Minister Benjamin Netanyahu has, with evident distaste, bowed to U.S. pressure to talk of negotiating the creation of a Palestinian state, but only if it is demilitarised and if Palestinians recognise Israel as a Jewish state.
Palestinians see this demand as prejudicing the claims to return or compensation of refugees displaced in the 1948 war over Israel's creation, and as undermining the status of Israeli Arabs who make up a fifth of its population.
They, and many Arabs, are also aggrieved that Obama now asks only for Israeli restraint on expanding settlements, which are illegal under international law and threaten the viability of any Palestinian state, instead of the freeze he earlier sought.
Palestinian President Mahmoud Abbas, whose credibility has been strained by his own policy zigzags and vulnerability to U.S. pressure, rules out renewed negotiations before an Israeli settlement freeze, as mandated in a 2003 U.S.-backed peace plan.
James Dobbins, director of the Center for International Security and Defense Policy at the RAND Corporation in Washington, said the chances of advancing were very slight.
"The Israeli government doesn't really want a settlement on the basis that most of the international community could support, let alone the Palestinians," he said.
"And the Palestinians, although they might want a settlement on those grounds, probably couldn't carry their population."
Dobbins said he expected the Obama administration to keep trying, if only to demonstrate that any failure could not be attributed to a lack of American commitment or involvement.
"It doesn't cost them anything," he added.
Whatever else is preoccupying Obama at home and abroad, he is unlikely to abandon the quest, said James Pickup, a former colleague of the president's Middle East envoy, George Mitchell.
"This administration sees itself as being able to multi-task and the peace process is viewed as critical to U.S. national security interests, so they will continue to put a lot of resources, time and effort into solving it."
That goal has eluded several U.S. presidents and countless other mediators, even though conventional wisdom holds that the inevitable outlines of a two-state solution are now well-known.
But Obama's diligence and determination may bring that solution no closer, said Rob Malley, the International Crisis Group's Middle East and North Africa Program Director.
"At some point the administration has to face the fact that however much it tries to improve the atmosphere and to work on some of these issues, the gaps between the two sides today are greater than they were yesterday, and yesterday they were too great to be bridged," he told Reuters in Washington.
"So in my view there needs to be a deeper rethinking of the peace process that goes beyond saying we are going to be more engaged, tougher and better intentioned."
Malley identified an aspect largely ignored in previous talks over borders, settlements, Jerusalem and refugees.
"There is deep down an emotional, political, psychological conflict between Israelis, who feel their right to have a state in what Jews consider their ancestral homeland has never been truly recognised, and Palestinians, who sense that all these negotiations are ultimately designed to erase their own history and their own claims that are born out of 1948."
Malley said tackling this gulf might not lead to a solution, but noted that 16 years of U.S.-backed peacemaking had failed.
"Trying to understand what piece of the puzzle has been missing seems to me more fruitful than simply once again heading down the same path." (Additional reporting by Dan Williams in Jerusalem; Editing by Samia Nakhoul)