''Negotiations have worked, can work, and we must see to it that they work again,'' George Shultz told guests at his State Department luncheon Friday in honor of Egyptian President Hosni Mubarak. Shultz added that the United States believes, as it has always believed, that direct negotiations among the parties to the Arab-Israeli conflict is the way to peace. And he added the United States ''will pursue any avenue to get to that end, including an international conference.''

It was something new. Shultz had never been so affirmative about an international conference. And his comments made it clear that his ''intense discussions'' with Mubarak had had an impact on American Mideast policy.

Egypt's president had come to Washington not only to discuss his country's economic problems but also to make the case for a new beginning in the troubled relations between Israel and its Arab neighbors. In conversations with Americans in and out of government, Mubarak argued that disorder in the West Bank and Gaza added new urgency to the problem and has made it clear to all parties that the existing situation is not viable.

Throughout his visit, Mubarak called for a ''six-month moratorium on all forms of violence and repression,'' and he cautioned against being limited by ''old formulas'' and ''old ideas'' that have not worked. He also urged the organization of an international conference existing of all parties to the dispute (Israelis, Jordanians, Egyptians, Palestinians, Syrians) and the permanent members of the U.N. Security Council (the United States, the Soviet Union, China, France and Britain).

While Mubarak refused to talk on the record about the specifics of his proposal, private conversations with other members of his party indicated that he has, in effect, moved away from the Camp David formula for dealing with the occupied territories. Without formally renouncing the accords, the Egyptian government reportedly has concluded that the Camp David approach is not useful.

In the Egyptian view, the same hostility to the Camp David agreement that led other Arab nations to ostracize Egypt makes it desirable for pragmatic reasons to find new ways of approaching the problem. In that view, an international conference would be such a new departure.

Since Jordanian King Hussein feels he cannot publicly speak directly to Israel, then -- say the Egyptians -- let his negotiations with Israel take place in the framework of an international conference.

The multiple difficulties involved in organizing and conducting such a conference do not seem to greatly disturb the Egyptian president nor his foreign minister, Esmat Abdel Meguid. Those problems include:

Would the Soviet Union agree that the parties directly concerned constitute small negotiating groups? Would the Soviets agree that decisions could be made by the parties concerned, or would they insist (as they have) that all decisions be made by majority vote of the whole conference? Would Syria seek to sabotage an agreement among Israel, Jordan, Egypt and the Palestinians? Would the PLO sabotage an agreement that provided secure borders for Israel? Could Israel conceivably protect its vital interests in such a conference? Would not Israel and the United States be quickly isolated?

The Egyptians seemed to say that all these questions could be dealt with constructively in the context of the conference and should not be dwelled upon in advance.

Act now, worry later, they urged. The existing situation is ''very dangerous,'' members of the president's party reiterated, and will deteriorate further if no constructive action is taken. Life will become more disagreeable and dangerous for Israel, the United States, Egypt and Jordan, they predicted.

The time is now, Mubarak urged. He and his foreign minister believe it is very significant that Egypt has been readmitted to good standing in the Arab world while maintaining diplomatic relations with Israel.

Mubarak is a warm, confident and persuasive man who feels that the government of Egypt has demonstrated its fidelity to the Camp David agreements. He also feels his government can be trusted by all parties. His good faith is manifest. Perhaps this is why George Shultz sounded as if he were ready to embrace Mubarak's new departure.

Could it work? Could Israel take the first steps desired by the Egyptians? Those steps include halting all forms of violence, freezing all settlement activities in the West Bank and Gaza, respecting the political rights of Palestinians under Israeli occupation, ensuring the safety and protection of Palestinians ''through proper international mechanisms'' and moving toward an international peace conference ''with the aim of reaching a comprehensive peace settlement that provides for the recognition of the right of all states in the region to live in peace and for enabling the Palestinian people to exercise their right to self-determination.''

The first three steps seem relatively easy, the fourth and fifth much, much more difficult. Consigning protection of Palestinians to ''proper international mechanisms'' would require sharply curtailing Israel's jurisdiction over the territories. Organizing a conference with the aim of ''enabling the Palestinian people to exercise their right of self-determination'' means, in the semantics of the issue, agreeing to the establishment of a Palestinian state in exchange for ''recognition'' of Israel's ''right to live in peace.''

Successive Israeli governments have said that a Palestinian state is incompatible with Israel's peace and security. But then, ruling indefinitely a sullen and sometimes violent population is also incompatible with Israel's security, and with its democratic principles as well. And it is always barely possible that, given self-determination, Palestinians might choose federation with Jordan instead of becoming a PLO state.

To cut the Gordian knot, Israel just might find it worthwhile to move toward an international conference, providing of course that it has a clear advance understanding with its American friends. Nothing is easy in the Middle East.