Washington — The United States and Israel have begun a process of improving relations that may require many more months of negotiation. Two days of high-level US-Israeli talks in Washington appear to have produced agreement on more grant aid to Israel, more cooperation over Lebanon, and more Israeli-based backup support, such as medical facilities, for US armed forces operating in the Middle East.
The US is also to resume delivery to Israel of cluster-bomb artillery shells.
But disagreements persist over President Reagan's 1982 peace plan, over Israel's West Bank settlements, and over American arms sales to Arab nations such as Jordan and Saudi Arabia.
In sum, Israel appears to have gained the most in terms of an immediate payoff from the talks here, particularly in terms of aid. But Secretary of State George Shultz and other officials who have led the drive for improved relations with Israel are apparently going on this assumption: that by helping to relieve Israel's fears about its own security through greater military cooperation, the US will over the long run gain more sympathy for its views from Israel.
The short-run payoff for the US could come in Lebanon, where the US and Israel might be able to cooperate in making life easier for the hard-pressed president of Lebanon, Amin Gemayel. According to some experts, this will depend mainly on the US ability to get the Israelis to be flexible about implementation of last May's Israel-Lebanon agreement on the withdrawal of foreign forces from Lebanon.
President Gemayel is reported to want modifications in the agreement, or at least a freezing of its political provisions, including a normalization of relations with Israel. He is apparently prepared to argue that this would facilitate a reconciliation with Syria and with the Lebanese factions that oppose him. Syria has been demanding that the Israel-Lebanon agreement be scrapped. Gemayel is scheduled to arrive here this evening for talks with President Reagan tomorrow.
In the recent past, senior Israeli officials have stated that they would not accept ''any basic change'' in the agreement with Lebanon. But that would seem to allow for some revision of the agreement.
All of this is of great importance to the Reagan administration, because a reconciliation among Lebanon's warring factions might permit withdrawal of the US Marines from Lebanon. All indications are that in the coming election year, pressure will increase from Congress and White House political advisers for a withdrawal of the highly vulnerable Marine contingent.
The administration is hoping that by presenting a united front with Israel on Lebanon, it will be able to contain Syria's strong influence in that nation. But some experts outside the administration doubt that this approach will have much affect on the battle-hardened Syrians.
''The notion that we can shake an Israeli stick at the Syrians and make them terribly afraid'' is not valid, says William B. Quandt, the former Middle East director for the National Security Council staff under the Carter administration , now with the Brookings Institution.
''The Syrians have a lot of respect for Israeli military strength, but they know that the Israelis have used that strength with some prudence when it comes to Syria.
''The idea that some people have that we can change the Israelis into our Cubans overnight is an illusion,'' says Mr. Quandt. ''The Israelis approach the Middle East with different concepts and different interests from the United States, and those are never going to go away. . . . Israel is an independent country. It's not a satellite.''
Quandt argues that every recent administration has tried out the theory of increasing Israel's sense of security in order to gain Israeli cooperation on major issues, only to come to the realization that there can be no trouble-free relationship with Israel. To expect the Israelis to be more accommodating on the issue of West Bank settlements would be an illusion, Quandt says. But he is among those who believe that common ground with Israel can be found when it comes to dealing with President Gemayel and Lebanon's much-troubled reconciliation process.
But even here there could be difficult problems. An Israeli official said to modify the Israel-Lebanon agreement would ''show a sign of weakness - just the wrong signal to send to the Syrians.''
Reagan administration officials hope that increased consultation with Israel will lead to fewer surprises in Lebanon. Israel's June 1982 invasion of Lebanon threw top administration officials into near disarray. The drive into Beirut that followed the invasion was taken against American wishes. So was the Israeli withdrawal from Lebanon's Shouf Mountains in this fall.
Within the administration, critics of these Israeli actions argue that Israeli's entry into the Shouf disrupted the Lebanese balance of power there, and that its subsequent withdrawal created a vacuum and triggered a new eruption of factional fighting.
Yitzhak Shamir's visit here this week was the first by an Israeli prime minister in 11/2 years. So there has been much to discuss.
But the Israelis were apparently not pleased that the Americans insisted on placing on the agenda discussion of the Reagan peace plan, the West Bank settlements, and the American need to improve ties with friendly Arab nations.
A State Department official argued that being friends or members of the same ''family'' means being able to raise any question for discussion, no matter how disagreeable that question might be to one party or another.
Despite Israeli objections, the Reagan administration has not given up its plan to finance and supply a Jordanian intervention force to help secure Gulf oil supplies should a crisis erupt in that key part of the Middle East. The Israelis contend that US weapons supplied to Jordan for the Gulf could be turned westward, against Israel.