America's main pro-Israel lobby group is mobilising members of Congress to pressure the White House over its bitter public confrontation with Binyamin Netanyahu, the Israeli prime minister.

The move, by the American Israel Public Affairs Committee (Aipac), appears aimed at exploiting differences in the Obama administration as it decides how to use the crisis around settlement building in Jerusalem to press Israel towards concessions to kickstart peace negotiations.

Aipac has persuaded more than three-quarters of the members of the US House of Representatives to sign a letter calling for an end to public criticism of Israel and urging the US to "reinforce" its relationship with the Jewish state.

The open letter, which has been circulating among members of Congress for the last week, says that while it is recognised that there will be differences between the two countries, they should be kept behind closed doors. "Our view is that such differences are best resolved quietly, in trust and confidence," it says.

The public differences, and revelations of Obama's private snubs of Netanyahu at the White House last week, have proved embarrassing to the Israeli leader at home, where he has been accused of undermining Israel's most important relationship.

Signatories to Aipac's letter include Steny Hoyer, the Democrat majority leader, and Eric Cantor, the Republican whip. The wording is similar to an email Aipac sent out during Netanyahu's visit, describing Obama's criticisms of the Israeli government as "a matter of serious concern" and calling on the US administration "to take immediate steps to defuse the tension with the Jewish state".

But while Aipac has for years influenced US policy on Israel, by targeting members of Congress who criticise the Jewish state, it may no longer have the same impact.

Robert Malley, a former special assistant to President Bill Clinton for Arab-Israeli affairs, said the administration's decision to take a once routine disagreement over settlement construction in East Jerusalem and turn it in to a confrontation is a reflection of the determination in the White House.

"This episode tells us more about the past and the future than the present. It's a reflection of the accumulated frustration and mistrust of the Netanyahu government by the White House. For the future, they're headed for a collision on the pace and nature of peace negotiations," he said. "We're seeing determination."

A source, who is consulted by administration officials on Israel policy but did not wish to be named, said that having chosen to take Netanyahu on, Obama cannot afford to back away. "The administration's credibility is at stake – in Israel and the Arab world. Netanyahu thought he had the better of it last year after he humiliated the president by rejecting his demand for a settlement freeze. If the administration does not follow through on this, or reaches some compromise that takes the heat off the Israelis, I suspect it will be almost impossible for us to get anything off the ground," he said.

Netanyahu appears to have been caught off guard by Obama's stand, perhaps because he was overconfident of being able to bypass the administration by relying on strong support for Israel in Congress. But while Aipac has been able to mobilise support for its letter, Congressional leaders have remained largely silent on the substance of the dispute.

That is, in part, because there is little enthusiasm for Jewish settlements. In addition, the White House has played an unusual card in suggesting that Netanyahu's intransigence is endangering US interests in the Middle East, and the lives of US soldiers in Iraq and Afghanistan.

"So far, I've been surprised by how muted congressional reaction has been," said Malley. "It may come, but if the administration manages to portray this as an issue of US national interest, it may be able to sustain a level of criticism."

However, there are reports of divisions within the administration on how to proceed. The US special envoy to the Middle East, George Mitchell, and the national security adviser, James Jones, believe Israeli governments respond to pressure. Last year an Israeli diplomatic memorandum described Jones as having told European officials that the US administration would take a hard line with the government in Jerusalem. Some officials favour mapping out a blueprint for peace and pressing both sides to adopt it.

But other officials argue against forcing Netanyahu to make compromises that will bring down his rightwing coalition. There has been criticism from Dennis Ross, who served as Bill Clinton's Middle East envoy. Now a Middle East strategist for the Obama administration, he is reported to be arguing for the White House to ease up on Netanyahu. However, Ross is regarded by some sceptics as too close to Israel. He has publicly argued that Jerusalem must remain undivided and is regarded with suspicion by the Palestinians, who saw him as effectively negotiating on Israel's behalf, rather than as a neutral mediator.

Malley says that whatever the Obama administration does it is almost certain to lead to further confrontation with the Israeli government. "The next crisis is more or less inevitable, given the diverging views of the Israeli and US governments on the pace and direction of the emerging talks," he said.