Pressure is mounting on Benjamin Netanyahu, the Israeli prime minister, to bring the opposition leader Tzipi Livni into the government after last week’s difficult meeting with the US president, according to senior analysts.

Yaron Ezrahi, a political science professor at Hebrew University in Jerusalem, said Mr Netanyahu now understood that he faced a stark choice between clashing with the White House and ditching the far-right parties in his coalition.

During the talks in Washington, Barack Obama said he expected an immediate halt to settlement building, a move rejected by Mr Netanyahu’s main coalition partners and many in his own right-wing Likud Party.

The Israeli prime minister hinted this week he will probably renew the call for Ms Livni, the leader of Kadima, a centrist party, to join the coalition after his failure to tempt her into a unity government following February’s general election.

Highlighting the alleged threat of Iran’s gaining a nuclear warhead as the main danger facing Israel, he told his party on Monday the priority was to “reach as broad a national unity as possible to repel the danger. Our relations with the United States are important and we must preserve them”.

Prof Ezrahi said: “As long as Netanyahu didn’t know how obstinate Obama was going to be, he could afford to ignore all the signs coming from the White House. But after the talks in Washington, Netanyahu’s hand is considerably weaker.

“Netanyahu and Livni are now indispensable to each other.”

Tensions within the current coalition have mounted over the past week, particularly over indications that Mr Netanyahu may try to dismantle a handful of tiny outpost settlements as a minimal concession to the US administration.

The White House is demanding an immediate freeze on all settlement expansion in the West Bank to prepare the ground for a peace deal with the Palestinians.

Mr Netanyahu is opposed to the creation of a Palestinian state and is offering a much vaguer “economic peace”.

Yesterday, Dan Meridor, the intelligence agencies minister, met US officials in Britain in what the Israeli media described as an attempt to persuade the White House to allow continued expansion of the larger settlements in return for a crackdown on two dozen outposts.

Ehud Barak, the defence minister and leader of the much-diminished left-wing Labor party, is expected to convey the same message on a trip to Washington next week.

Last Thursday Mr Barak sent in security forces to dismantle one outpost, Maoz Esther, east of Ramallah, that consisted of five huts and two tents. There are more than 100 similar outposts across the West Bank, ostensibly unauthorised by the government and housing a few thousand settlers.

On Monday Mr Barak also approved “zoning notices” against a further 10 outposts, setting in motion proceedings that could eventually lead to their demolition.

He promised to dismantle a total of 26 outposts, a pledge Israel made to the previous US administration of George W Bush but has yet to fulfil.

Observers, however, were largely unimpressed by the supposedly tough new stance. It was the fourth time Maoz Esther has been dismantled and, as on previous occasions, the settlers were allowed back a few hours later.

Uri Avnery, leader of the Gush Shalom peace group, accused Mr Barak of conducting only “a performance of ‘demolishing outposts’”.

Nehemia Strasler, of the liberal Haaretz newspaper, argued that the spectacle was meant to “divert [US] attention from the construction taking place all over the West Bank”.

At a cabinet meeting on Sunday, the right-wing parties vied in denouncing Mr Barak, with one calling his move a “witch-hunt” against the settlers. The next day Mr Netanyahu tried to reassure his party by suggesting the crackdown on outposts would win US backing for Israel’s hard line on Iran.

Writing in Haaretz, Aluf Benn, another columnist for the paper, noted: “Netanyahu is in a trap: the more he tries to persuade Obama he can provide the diplomatic goods, the quicker his coalition will expire.”

Mr Netanyahu’s only saviour, according to Prof Ezrahi, is his chief rival for power, Ms Livni. He said the Israeli public expected unity from senior politicians during times of crisis and neither Mr Netanyahu nor Ms Livni would want to be seen wrecking the chances of a unity government.

“Israelis believe the country’s existence totally depends on US support and will judge harshly any leader who risks jeopardising that relationship. That is the most pressing political constraint on Mr Netanyahu.”

Ms Livni added to the pressure on Mr Netanyahu this week. She accused him of “bad management” and said Israel was “witnessing signs of a diplomatic collapse”.

Yesterday she criticised the government’s preference for the road map, a US peace plan from 2003, saying it delayed direct talks with the Palestinians for too long.

“Refraining from talking will bring us to a situation in which we won’t have a partner for talks,” she told Army Radio.

Ms Livni faces her own political constraints. Shaul Mofaz, her main challenger to lead Kadima, has been lobbying among colleagues against her earlier refusal to join the coalition.

He added that most Kadima legislators privately agreed with him on the need for a unity government.