Israel's decision not to retaliate for Iraq's missile attacks was influenced strongly by President Bush's pleas and advice from U.S. supporters who said the Jewish state is winning priceless international goodwill and improved relations with the United States, U.S. and diplomatic sources said yesterday.

The sources said the Bush administration is less worried than it was that Israeli entry into the Persian Gulf War would splinter the U.S.-led coalition against Iraq but remains concerned that it could trigger a conflict with Jordan that would threaten King Hussein's monarchy, the sources said.

Last night, Bush dispatched Deputy Secretary of State Lawrence S. Eagleburger and Defense Undersecretary Paul D. Wolfowitz to Israel "to discuss with the Israeli government the situation in the region" in light of the Scud attacks, White House spokesman Bill Harlow said.

"We're very pleased by the Israeli government's continued forbearance, but it's a moment-by-moment situation that could change at any time," particularly if there are new Iraqi attacks that cause Israeli deaths, said a senior U.S. official. No Israelis have been killed by the missile attacks Iraq launched yesterday and Friday.

"There's still a great deal of hand-holding to do," the official added in reference to Bush's two phone calls yesterday to Prime Minister Yitzhak Shamir. "In all the contacts, our message is unchanging and clear: We tell them we know they are under great strain and provocation, but we think that these attacks can't go on for too much longer and that Israel can make a greater contribution to the goal of defeating Iraq by continuing to show restraint."

Other sources said American Jewish organizations and Israeli supporters in Congress have told Shamir's government that Iraq's attack on Israeli population centers and its calls for a massive Arab rising against the Jewish state are creating sympathy for Israel here and in Europe.

The sources said this sympathy could play a major role in reversing the widespread impression in this country that the Shamir government has been unduly harsh and inflexible in dealing with the three-year uprising among Palestinians in the West Bank and Gaza Strip.

"For the first time, I have heard people who are not normally supporters of Israel saying, 'Hurrah for Yitzhak Shamir,' " said an official of one Jewish American organization.

"{Iraqi President} Saddam Hussein has given the Israelis the best forum they've had in years for making the argument that their reluctance to give up the occupied territories is due not to a desire to subjugate the Arabs but to legitimate concern that they cannot entrust their security to promises by the Palestine Liberation Organization and its patrons like Saddam that the Arabs have put aside their vow to erase Israel completely from the map of the Middle East," he said.

Israel's practice of not allowing any attack to go unanswered always has been a tenet of its defense policy. The sources said that by not retaliating, at Bush's request, Israel will be in position to expect greater U.S. backing and understanding when new calls are made in the aftermath of the gulf crisis for Israeli concessions to resolve the Palestinian question.

Even if new Iraqi missile attacks prompt Israel to drop its forbearance, U.S. officials said they feel reasonably sure continued Arab participation in the coalition will not be seriously undermined.

Two of the three principal Arab members, Egypt and Saudi Arabia, have said they would not object if an Israeli strike clearly was retaliatory. Even Syria, the most hard-line opponent of Israeli involvement in the conflict, has hinted recently it now would take a similar position.

Syria has approximately 20,000 troops with the coalition force but has said they will be used only to defend Saudi Arabia.

"The threat of Israel breaking up the coalition was probably overstated in the first place," one U.S. official said. "Now that the fighting has made clear that Iraq is hopelessly outgunned and can't win, no one wants to be on the losing side or even left behind."

Nevertheless, he and other officials stressed that the administration prefers that Israel stay out of the war in large part to prevent the complications that would ensue were Jordan, which has tilted toward Iraq, forced into the fighting. Because any Israeli air sorties undoubtedly would fly over Jordan, King Hussein's vow to resist invasions of his air space would mean clashes with Israeli aircraft that could escalate unpredictably.

Of particular concern, U.S. officials said, is the possibility that Palestinians, who comprise the largest part of Jordan's population, and Moslem extremists, who are gaining strength, might be incited to overthrow Hussein. That could provoke an invasion by Israel that would throw the entire region into turmoil and confront Washington's Arab allies with a serious dilemma about where their loyalties lie.