Israeli Prime Minister Shimon Peres today welcomed signs from King Hussein in Washington that the peace process still may be alive despite Israel's bombing Tuesday of the Palestine Liberation Organization headquarters in Tunisia.

But Peres said that Hussein's reported remarks in closed talks with a group of U.S. senators that no state of belligerency exists between Jordan and Israel and that Jordan recognizes Israel's right to exist -- are not enough.

"I take it as a good omen but not as a sufficient change which is necessary in order really to open a way for a continuation," Peres said. If Hussein means what he says, Peres suggested, he should say it on the record.

"State of war is an official, declared in full daylight, position of Jordan," Peres said. "And if Jordan is changing it it should be done in the very same way."

Answering questions at a Foreign Press Association lunch at the King David Hotel, Peres appeared confident despite the widely unfavorable response to the Israeli raid in Tunisia, including Egypt's decision to break off talks with Israel on a sensitive border issue.

Peres put aside the fact that U.S. officials have backed away from their initial unqualified endorsement of the raid.

President Reagan's remarks on Tuesday terming the attack an act of self-defense were "crystal clear," Peres said, regardless of U.S. attempts the next day to "deplore" the violence. Since Israel had taken into account the possibly negative international reaction before launching the raid, Reagan's remarks were "for us, shall I say, a refreshing surprise," Peres told reporters.

On the issue of Israeli-Arab relations, Peres said: "I am whole-heartedly for peace. I don't think that an Arab country that is ready to negotiate with us for peace is doing us a favor. We are not a charity organization. We don't do a favor to them when we seek peace, and they don't do a favor to us when they seek peace. They need it. We need it. They want it. We want it."

"I believe King Hussein wants peace. I believe King Hussein needs peace," Peres said, adding, "I hope that this momentum will be continued in spite of the many difficulties and many complications."

While Hussein reportedly has concluded he must have the support of PLO Chairman Yasser Arafat in order to move forward with the peace process, Peres insisted Hussein does not. Discussing the Tunisia raid in a television interview last night, he said, "I differentiate between relations with Jordan and the war on PLO terrorism." More generally, he added, "In my estimation Hussein is not happy with Arafat's entire activity."

The immediate cause cited was the killing of three Israelis in Larnaca, Cyprus, last week by three pro-Palestinian gunmen.

Peres was asked today about reports that the Israelis were Israeli intelligence agents, and not vacationers, as Israel has said. Peres said that the newspaper that said they may have been agents should run a correction.

He was asked how Israel knew that the men in Cypriot custody in the Larnaca murders were working for the PLO's special security wing, Force 17, as Israel charged in justifying its raid. Peres said they had been identified by some of the Force 17 members Israel captured off its coast last April, allegedly preparing for raids.

Peres also denied that the aim of Israel's raid was to kill Arafat.