Prime Minister Shimon Peres, speaking in the aftermath of the Palestinian hijacking of an Italian cruise ship, assured President Reagan yesterday that Israel still extends a "hand of peace" to Jordan and will consider any proposals from King Hussein for "honorable and direct negotiations."

Reagan said "there is a better opportunity for real progress than there has been for some time." But neither he nor Peres gave any sign that they have found a formula for removing the obstacles in the path of peace talks, and Secretary of State George P. Shultz acknowledged earlier yesterday that the Achille Lauro hijacking had made the search for solutions more difficult.

"With our hand of peace extended across the Jordanian River, we call upon our eastern neighbor to heed and accept this sincere invitation," Peres told Reagan following a White House meeting.

"We are ready to meet without any preconditions, without losing time and at a suitable location, be it Amman, Jerusalem or Washington," Peres said. "We are prepared to consider any proposal put forward by the Jordanians."

Neither Peres nor Reagan made any direct reference to the Palestine Liberation Organization, whose role in the peace process has been further complicated by U.S. and Israeli charges of PLO complicity in the Achille Lauro piracy that involved the murder of an American citizen.

Shultz, testifying before the House Foreign Affairs Committee yesterday, said that "the violence that has come from the PLO . . . provides greater clarity" about the PLO's apparent unwillingness to accept Israel's existence and forswear armed struggle against the Jewish state.

Shultz appeared to be hinting that events of recent days should cause Hussein to reconsider his agreement with PLO Chairman Yasser Arafat to seek some kind of role for the PLO in the negotiating process.

He argued that recent events have given Hussein a clearer picture of PLO attitudes. In that respect, Shultz cited the ship hijacking, the role of "people who are identified with the PLO" in the murder of three Israelis in Cyprus and the barring of two PLO members of a Jordanian delegation from a meeting with British Foreign Secretary Geoffrey Howe earlier this week because they refused to sign a statement recognizing Israel's right to exist.

"What King Hussein needs to find and, for that matter, what Israel needs to find is people who, regardless of their biographies, are ready to sit down in a constructive spirit, accept Israel as there, and try to work out arrangements under which there can be peace," Shultz said.

Another major sticking point involves Hussein's insistence that direct talks with Israel take place under the "auspices" of an international conference including the Soviet Union.

The Israelis have opposed that idea, but prior to Peres' arrival here, there were hints from Jerusalem that Israel might give on that point if the Soviet Union, which broke relations with Israel after the 1967 Middle East war, renews the ties.

A senior U.S. official refused to say whether that point came up in yesterday's talks. Israeli sources said that while there was some discussion of the idea, the Soviets do not appear to think it advantageous to recognize Israel at this time, particularly if the proposed international conference would only be a pretext for direct negotiations rather than a vehicle that would give Moscow increased influence in the region.