A backstage political coup to be attempted inside the Labor Party by one of Israel's most respected and powerful figures over the past 30 years could transform U.S.-Israel relations, now at their most frigid point since the Israeli invasion of Lebanon eight years ago.

Former prime minister Yitzhak Rabin has told friends he will seek to oust Labor Party leader Shimon Peres before the end of June, pass a no-confidence motion in the Knesset to overthrow the new right-wing Likud government and then go to elections. His platform would commit Labor to a peace plan similar to the U.S. proposals rejected by Likud.

When the deal we described last week collapsed and Likud's right-wing Prime Minister Yitzhak Shamir abandoned plans to renew the old Likud-Labor unity government, Rabin began planning his political move to strip the mantle of leadership from Peres and put it back on his own shoulders. He lost it in 1977 when, as prime minister, he was dragged into a minor political scandal and Peres took over.

For the United States and Israel, Rabin's move has immense stakes. President Bush regards Shamir as a barricade to Israel-Palestine peace, chilling U.S.-Israel relations. Fears of a new Mideast war are rising as Arab states build new weapons almost as lethal as Israel's nuclear missiles, but Bush and Secretary of State James Baker have been unable to lure Shamir into their peace process.

Enter Rabin. His lofty goal of becoming prime minister and heading a government committed to serious peace talks with Palestinians would be written off as a romantic, even dangerous, ambition except for two factors.

First are the polls that show him to be the most popular politician in Israel, a country where everybody considers himself a politician. His public standing rests on his military exploits, going back to the war for independence and on his reputation for no-nonsense straight talk in a party that has had weak leadership for years.

Second is the pervasive pull of the U.S. connection, a mystical and material bond based on shared values and billions of dollars in aid. Rabin's U.S. popularity is well-known in Israel, giving him a political cutting edge with Israelis worried about frayed American relations under Shamir.

Sympathetic officials in the White House and the State Department are watching this Rabin political move closely, but no one will speculate or cheer him on publicly. Comment by the United States could bring damaging Israeli accusations of interference in domestic affairs, backfiring on both Rabin and the Bush administration. But privately, in one influential downtown quarter, the Labor Party's Rabin is described as Israel's throwback to the late senator Henry M. (Scoop) Jackson, a liberal Democrat whose views on foreign policy were acceptable to hard-liners.

''Shamir is able to risk peace, but not willing,'' one source told us. ''Peres is willing but not able. Rabin is willing and able.'' Rabin, in New York for a few days last week, told us that the peace process ''has been freezed. And this is what worries me as an Israeli.''

Alone in the Labor Party, it is Rabin who commands respect even among Likud hard-liners who do not share his optimism for launching serious talks with Palestinians over the future of the West Bank and Gaza. What partly earned him that respect was his tough policy at the outset of the intifada to encourage harsh intimidation -- clubbing and limb-breaking -- while ruling out lethal punishment by the Israeli army.

On Capitol Hill, Rep. Mel Levine (D-Calif.), a leader of the pro-Israel congressional bloc, said he agreed with Rabin that ''pursuit of the peace process'' must be continued. He told us that some Israelis are convinced ''that some combination of Rabin and Shamir could bring this about.''

But Rabin believes the time for such a combination has passed Shamir by. Moreover, he is now pushing for a fundamental change in the election of prime ministers. Up to now, the head of the party that gets the most votes automatically has become prime minister. Rabin wants the prime minister elected by popular vote. For the most popular politician in Israel, that makes sense.