Secretary of State George P. Shultz ended his three-day mission to the Middle East today, saying that "some headway" has been made toward new Arab-Israeli peace negotiations, but acknowledging that "many difficulties" remain.

Shultz made his comments in Aqaba, Jordan, after a final round of meetings with King Hussein and in an interview with reporters while flying to this Austrian capital, where he is to meet Soviet Foreign Minister Andrei Gromyko Tuesday.

Shultz gave no details of the "headway" he claimed. Moreover, he refused all but the most roundabout comment on how he and Hussein propose to surmount the immediate roadblock to new negotiations: the naming of Palestinian representatives acceptable to both the Palestine Liberation Organization, on the one hand, and the United States and Israel on the other.

Shultz, who is rarely forthcoming about his diplomatic dealings, reached a new level of mysteriousness in his descriptions of the state of the effort to find Palestinian participants.

He denied that he had discussed the names of specific candidates, although Jordanian officials said names had been submitted to him in advance. The farthest he would go in explaining the headway he claimed was to say that he and Hussein discussed "the nature of the difficulty" of identifying acceptable Palestinians.

The guarded comments of Shultz and other U.S. and foreign officials along his quick tour of Israel, Egypt and Jordan left the impression that his tour more than anything else etched in sharp relief the conflict in views among Israel, Jordan, the PLO and to an extent the United States, about Palestinian participation in a new Middle East negotiating process, and the very narrow area for accommodation.

Shultz described as "a plus" the statement of the Israeli Cabinet yesterday opposing the participation in negotiations of any Arabs who are committed to the charter of the PLO. That statement, which arose from the weekend meetings with Shultz, would seem to place a further restriction on potential Palestinian participation, but Shultz said he took heart because the statement did not explicitly say that any member of the Palestine National Council, which originated the charter, would be disqualified as a negotiator.

According to a senior Jordanian official, all of the Palestinians whose names were submitted to the United States in advance of Shultz's trip are members of the Palestine National Council, the PLO's parliament in exile.

"I don't think its our role" to discuss particular candidates with Hussein, Shultz told reporters. At the same time though, he said that "at the final moment it is the names of people suggested as negotiators who count."

To report on his discussions, Shultz sent Assistant Secretary Richard W. Murphy, his principal Middle East troubleshooter, back to Egypt and Israel, and on to Saudi Arabia and North Africa.

The next major step, Shultz said, could be expected to arise from Hussein's meetings with President Reagan in Washington at the end of this month.

A proposed new U.S. arms sale to Jordan, reportedly to include high-performance warplanes, troop-carrying helicopters, surface-to-air missiles and other weapons, is likely to turn on the Reagan administration's ability to argue that Jordan is playing an important role in a drive for peace with Israel.

Abandonment of the peace initiative begun by Hussein in his "framework" agreement Feb. 11 with PLO leader Yasser Arafat would damage the already uncertain prospects that Congress would approve an arms sale to Jordan, which is opposed by Israel.