JERUSALEM, Sept 12 (Reuters) - The public row between Israel and the United States this week will make it hard for Prime Minister Benjamin Netanyahu to launch a unilateral strike against Iran and risks undermining his domestic standing.

Despite years of warning about the dangers of Iran gaining nuclear weapons, the Israeli leader has failed to convince any major world power of the need for military action and has yet to persuade his domestic audience that Israel should go it alone.

By raising the stakes with Barack Obama in the middle of the president's re-election campaign, Netanyahu has drawn criticism from his own defence minister, Ehud Barak, and given Tehran the pleasure of watching its enemies argue over the case for war.

"Netanyahu is overplaying his hand and creating problems for himself with Obama. This could make life very hard for him should the president win re-election," said Alon Liel, a former director-general of the Israeli foreign ministry.

Infuriated by Washington's reluctance to lay down clear limits to Iran's nuclear programme, Netanyahu fired a broadside at Obama on Tuesday, saying those who failed to set red lines did not have the "moral right" to prevent Israel from striking.

Further stirring the troubled waters, senior Israeli officials briefed journalists twice in two days to denounce U.S. policymaking, before announcing that the president had refused to see Netanyahu when both will be in New York later this month.

The White House denied ever receiving a request for a meeting and Obama swiftly got on the phone for a long chat with Netanyahu, with whom he has notoriously testy relations.

In the hours that followed, Israel sought to play down the differences between the two, but the damage was done, with the Israeli press bemoaning a new low in bilateral ties.

"The reality might be less serious than all the headlines are saying," said Oded Eran, a senior research associate and former head of the Institute for National Security Studies.

"However, perceptions are just as important, and in that regard, serious damage has been done to the idea of Israeli deterrence, which may be very hard to rectify," he added.

HOLDING BACK

Israel, believed to have the only nuclear arsenal in the Middle East, has long threatened to attack Iran unless it dismantles its ambitious nuclear programme that many countries in the West believe is aimed at creating an atomic bomb.

Iran denies this and, despite increasingly severe economic sanctions, has shown no sign that it intends to scale back its project or halt its contested uranium enrichment drive.

Regularly beating the drums of war, Netanyahu has succeeded in getting alarmed Western allies to turn the sanction screws, but has yet to persuade them of the need for military action, or even to win their backing for a lone Israeli initiative.

"The Israeli frustration stems from a sense that sanctions and negotiations are not as effective as they should be," said Gidi Grinstein, founder of the Reut Institute think-tank.

"But Israeli action in defiance of the United States and without legitimacy is extremely risky."

Aware that its armed forces might be hard pressed to do significant damage to Iran's far-flung nuclear sites, Israel has said repeatedly that it wants the U.S. military to do the heavy lifting, arguing a nuclear Iran is a threat to the whole world.

But rather than bow to Israeli demands for further clarity, U.S. Secretary of State Hillary Clinton has said Washington would not set any deadline with Iran. Her comments triggered fury in Netanyahu's office.

"The easiest thing would be to sit by and not tangle with Obama, but Netanyahu believes he has to state things plainly, even if they are unpopular and cause conflict," said a senior Israeli official, denouncing "fuzzy remarks" out of America.

INTERNAL, EXTERNAL CRITICISM

Yet Netanyahu might come to rue his outspokenness.

Israelis know the United States is by far and away their most important ally and previous premiers who jostled in public with Washington have invariably drawn flak at home.

Sure enough, Israeli opposition politicians have denounced the prime minister's handling of an increasingly complex situation.

"Who are you trying to replace? The administration in Washington or that in Tehran?" said Shaul Mofaz, head of the largest opposition party, Kadima, which was briefly part of Netanyahu's coalition over the summer.

"The world is not sick of Israel, the world is sick of Netanyahu and does not believe him."

Of more concern to Netanyahu was the fact he also received a clear rebuke from his own defence minister, Barak, who issued a statement saying problems with the United States should be worked out behind closed doors and not aired in public.

"Despite the differences and the importance of maintaining Israel's independence of action, we should also bear in mind the importance of the partnership with the United States, and try not to harm it as much as possible," he said.

Local media said Netanyahu was angered by Barak's intervention and a senior member of the prime minister's Likud party accused the defence minister of looking to score political points at a time of growing speculation about the prospect of an early parliamentary election in Israel.

Barak heads the small Atzmaut party in the governing coalition, and opinion polls have indicated it might not win a single seat in parliament in a new ballot.

"I am sorry that ... the defence minister has chosen to start his campaign at the expense of national interests and on the back of the prime minister," said vice prime minister Moshe Yaalon, who has long aspired to the defence portfolio.

Barak's spokesman denied any rift with Netanyahu, but again, the damage was done, with the two men who must work closest together on Israel's military strategies seemingly at odds over how best to proceed.