Secretary of State George P. Shultz has told Israel that King Hussein of Jordan is committed to direct peace negotiations with Israel and hopes the talks can begin this year, Israeli government officials said today.

Shultz, reporting on Hussein's talks with U.S. officials in Washington last week, made this assertion in a letter to Prime Minister Shimon Peres that was delivered last night, the officials said.

According to Israeli sources, Shultz characterized Hussein's position as going well beyond that to which any Arab leader, except those of Egypt, has been willing to commit himself publicly.

They said Shultz reported Hussein's willingness to enter direct negotiations with Israel on the basis of U.N. Security Council Resolutions 242 and 338 and that Hussein said this position was shared by Yasser Arafat, chairman of the Palestine Liberation Organization. The U.N. resolutions call for Israel to withdraw from territories captured in the 1967 Middle East war in return for peace with its Arab neighbors.

Israeli reaction to the Shultz letter, which was outlined by Peres at today's weekly Cabinet meeting, was mixed but largely skeptical.

The Israeli account of the letter indicated that Shultz backs the broad approach suggested by Hussein in his meetings in Washington last week. But aspects of that approach present problems for the Israeli government, and that could help to explain the lukewarm reaction from its Cabinet ministers, even those of the Labor Party.

In Washington, spokeswoman Kathleen Lang said the State Department had no comment on the reports of the letter.

According to the Israeli sources, Hussein remains committed to direct negotiations being held in the framework of an international peace conference that would include the Soviet Union. They said Shultz reiterated U.S. opposition to this proposal but suggested that efforts should be made to find some other "international context" that would give Hussein the necessary diplomatic cover to enter direct talks with Israel.

Israeli sources also said Shultz sent similar reports of Hussein's talks in Washington to America's NATO allies, suggesting that Washington may be seeking a formula that would allow peace talks to take place beneath a U.S.-European umbrella that would exclude Moscow.

A senior official from Israel's Labor Party, the main advocate of peace talks with Jordan within the government, said Hussein's talks with administration officials appeared to represent an "inching our way forward."

"I think it was a major breakthrough for Hussein in convincing Washington that this is as far as he can go and now he needs help," the official said.

A senior aide to Peres said, "There are some positive signs in that there seems to be an effort to bring about direct negotiations, but the negative side is that there are still too many obstacles. We are ready to go to direct negotiations tomorrow."

The reaction of the right-wing Likud bloc, the Labor Party's main partner in the national-unity government, was voiced by Trade Minister Ariel Sharon.

"I don't think Israel will accept it," Sharon said of Hussein's proposals as outlined by Shultz. Reiterating Likud's opposition to surrender of any of the West Bank and Gaza Strip, he added, "Israel, for peace with Jordan, will give only one thing: Israel will give peace and nothing more than that."

From the reports of the Shultz letter and the Israeli reaction, it appeared there are two major obstacles to peace talks between Israel and Jordan.

The first is Hussein's insistence on what one official here called an "international anchor" on which to base the risky step of becoming only the second Arab leader to enter direct negotiations with Israel.

The United States and Israel remain strongly opposed to Hussein's call for an international peace conference sponsored by the permanent members of the U.N. Security Council, which include the Soviet Union. But Hussein appears to have made progress in convincing the Reagan administration of his need for some international forum in which to begin the process.

Israel insists that only "direct talks" with Jordan will lead to peace, and finding a formula acceptable both to Hussein and the Israelis is likely to be difficult.

The second obstacle centers on the makeup of a joint Jordanian-Palestinian delegation to negotiate directly with Israel. Shultz made clear Friday after the Hussein visit that the United States is willing to meet with such a group as a preliminary step toward direct talks.

Israeli sources said that in his letter, Shultz said Hussein also was willing to view such a meeting as only a prelude to direct talks with Israel. But that left open the question of which Palestinians would be members of the delegation.

Israel has vowed never to negotiate with members of the PLO, and that position is supported by the United States. But amid the recent efforts to revive the peace process, the central question has become whether some members of the Palestine National Council, the so-called "parliament in exile," would be acceptable negotiating partners.

The Israeli government never has answered this question directly, but the assumption has been that Peres and other Labor Party ministers would be more flexible than their Likud partners. Foreign Minister Yitzhak Shamir, the Likud leader, has ruled out talks with a delegation including council members.