In the aftermath of the Iraqi missile attack on Israel, the United States is preparing to send Israel additional Patriot air defense missiles, administration sources said yesterday.

The decision came as the United States publicly thanked Israel for refraining from a retaliatory strike that could lead to a wider war and privately sought to assure Israel that American forces would redouble efforts to wipe out the Scud ballistic missiles and launchers that Iraq used to mount the attack Thursday night.

The officials said that Pentagon and State Department officials held intensive discussions with Israel over the last 24 hours about fulfilling the U.S. promise made last fall to retaliate on Israel's behalf for such a missile attack. The officials said it appeared that Israel would not retaliate immediately on its own, although Israeli officials said they refused to make any commitments to the United States and reserved the right to strike back at any time.

President Bush discussed the issue of retaliation in a telephone call with Prime Minister Yitzhak Shamir. White House press secretary Marlin Fitzwater said Bush told Shamir "he basically appreciated their restraint and asked for their understanding."

In a news conference, Bush vowed to carry out "the darnedest search-and-destroy mission that's ever been undertaken" to knock out Iraq's mobile Scud missiles. The United States has been tracking the missiles for months and is hoping to annihilate the force but they said they have not yet destroyed the known total of Scud missiles.

Administration officials have in recent months worried that a full-scale Israeli involvement in the conflict would threaten the participation of Arab members of the coalition, but Bush expressed confidence "this coalition is not going to fall apart."

The Iraqi missile attack came amid a new round of diplomacy with coalition partners. Secretary of State James A. Baker III, who phoned Shamir right after the missile attack, met yesterday with Saudi Arabia's ambassador, Prince Bandar bin Sultan. Deputy Secretary of State Lawrence S. Eagleburger met with Egypt's ambassador, El Sayed A.R. el-Reedy, who said his country would remain in the coalition if Israel retaliated. Undersecretary of State Robert M. Kimmitt met separately with Israeli Ambassador Zalman Shoval.

Israel recently received two batteries of the Patriot air defense missiles, but its crews have not finished training to use them. The missiles provide points of defense against incoming ballistic missiles, but the sources said Israel needs additional coverage of its borders against such an Iraqi attack. However, the sources said, this need is extremely sensitive for Israel, which does not want to advertise its vulnerability.

A Patriot missile successfully destroyed a Scud missile targeted on Saudi Arabia on Thursday night, but none of the Israeli Patriot missiles were used. U.S. officials said they could not discuss the reasons why.

Prior to the gulf crisis, there had been discussion about U.S. sale of the Patriot to Israel, but Israeli military planners were unsure about whether they wanted to use their limited resources on this expensive and relatively untried weapon.

Diplomatic sources familiar with the exchanges over the last two days between Washington and Jerusalem said the United States had repeated its argument that an Israeli retaliation would play into Saddam's hands, giving him a propaganda weapon and causing logistical problems for allied forces.

However, the sources said, the Shamir government steadfastly refused to rule out retaliation. The sources said the Americans were told a second Iraqi strike would leave Israel no choice but to respond.

But, the sources continued, if Iraq does not launch a second attack, Israel appears willing to wait Bush told Shamir "he basically appreciated their restraint . . . "

-- Marlin Fitzwater

and see if the renewed American bombing can eliminate the Scud threat. The sources said there were no promises and they stressed that the situation can change literally from hour to hour.

In fact, some sources said, what the Israelis told the Americans privately was much the same as they said publicly. Israeli Foreign Minister David Levy's public statement -- that it is "the prerogative and responsibility of Israel to decide how best to defend the citizens of Israel" -- was "an accurate reflection" of the stance Shamir took in his talks with Baker, according to a source.

"What Shamir said to Baker was, 'I hear what you're telling me and I will give it the utmost consideration,' " according to the source. " 'But I can make no promises.' "

Several sources said that unless a new attack from Iraq forces them to act, the Israelis appear to feel they can obtain some long-term political advantage from world revulsion at Iraq's Thursday attacks on civilian targets.Staff writer George C. Wilson contributed to this report.