Secretary of State George P. Shultz and King Hussein of Jordan met for more than two hours tonight but were unable to agree on Palestinian representation in new Arab-Israeli peace talks.

A senior U.S. official told reporters following the talks that "no breakthroughs are in sight" in dealing with "a whole set of problems that is extremely hard."

The Shultz-Hussein talks, following explorations by the secretary of state with the leaders of Israel and Egypt, are to continue Monday morning. But there was little expectation of immediate progress on the knotty issue of how Palestinians could be represented without giving any standing to the Palestine Liberation Organization.

A senior Jordanian official said before tonight's meeting that "about five" names of Palestinians nominated by the PLO to take part in the proposed negotiations were supplied to the United States last month.

All those listed, the official said, are members of the Palestine National Council, the PLO's parliament-in-exile.

Israeli Foreign Minister Yitzhak Shamir and a spokesman for Prime Minister Shimon Peres said Shultz was told in Jerusalem that Israel will refuse to negotiate with council members, considering them to be no different than officials of the PLO.

U.S. officials have indicated that Washington is less categorical in its view of the acceptability of council members and probably will judge them on a name-by-name basis.

But after tonight's Shultz-Hussein meeting, a U.S. spokesman said membership in the council has become "a contentious issue," suggesting that the U.S. position may have shifted somewhat after the meetings in Israel.

In Jerusalem, Cabinet Secretary Yossi Beilin quoted Peres as saying at a Cabinet meeting Sunday that "Israel is prepared to conduct direct negotiations with a joint Jordanian-Palestinian delegation which will not include persons belonging to an organization that is committed to the Palestinian covenant," Washington Post correspondent Edward Walsh reported. Beilin added, "We will not deal with those who are committed to destroying Israel."

This statement appeared to be a hardening of the Israeli position, which heretofore had been opposed to including only "declared members of the PLO" in any such delegation. The new statement appears to reflect opposition, expressed by both Shamir and Peres, to allow even members of the Palestine National Council who are not "declared PLO members" to be part of the delegation.

PLO Chairman Yasser Arafat, speaking to reporters in Peking where he and a joint Jordanian-PLO delegation met with Chinese leader Deng Xiaoping, said he and Hussein have agreed that "any delegation of any purpose or any mission has to be from the Jordan government and the PLO, directly."

Taunting the United States, Arafat, speaking in English, said the U.S. administration is "still looking at this very narrow angle, from this Israeli narrow angle. . . . They are still trying to hide the sun with their finger, neglecting realities and facts in this area."

The Jordanian official, who asked not to be named, said the central purpose of the Hussein-Shultz meetings is to narrow the list of proposed Palestinian negotiators to those acceptable to Washington. There was no indication following the initial meetings that agreement was in the cards. Nonetheless, a spokesman said that Assistant Secretary of State Richard W. Murphy, who has headed the drive for new negotiations, would remain in the area for a day or two after Shultz leaves at midday Monday to meet Soviet Foreign Minister Andrei Gromyko in Vienna.

Shultz told reporters traveling with him that "I'd rather not speculate about names, lists, categories, whatever."

At another point, Shultz defined the issue as finding "people who are truly recognized as able to represent Palestinians and who also have a background that will be acceptable in a negotiating process given all the history of absolute opposition to Israel."

Shultz began the day in Jerusalem in a meeting with Peres and a brief airport conference with Shamir. In Cairo, he met for two hours with President Hosni Mubarak, who originated the idea of a joint Jordanian-Palestinian conference with the United States as a first step toward peace with Israel.

Leaving Cairo, Shultz spoke again of "the hard problems" involved in the process and called for determination by all in the area "to work at the problems and to keep the level of frustration down and the level of effort up."