Secretary of State George P. Shultz says there are indications that Arab leaders may be taking a second look at President Reagan's Middle East peace initiative since Jordan's King Hussein announced two weeks ago that he was not ready to participate in negotiations with the United States and Israel.

"It does seem to me that there's a certain shock that has taken hold, as I read the cables from the various Arab capitals, in which people are saying to themselves, 'Are we really going to pass this up? Maybe we can't afford to do that,' " Shultz said in an interview Friday with the editor of the editorial page of The Washington Post.

"I think it's well for them to talk among themselves and see if they aren't missing the boat," he said.

Shultz is scheduled to leave here tonight for Cairo, where, he said, his primary concern will be to try negotiating removal of foreign troops from Lebanon, considered an essential first step in the broader effort to bring peace to the Mideast.

He said he hopes that his mission will lead to further discussions with Hussein, Saudi Arabia's King Fahd and the leaders of Syria, which has indicated it will withdraw its troops from Lebanon when the Israelis leave.

"Once a satisfactory agreement is reached with the Israelis --assuming that it will be reached, and I think that it's possible, all right--then we have to say to the Syrians, 'All right, the Israelis have agreed to withdraw, now it's up to you,' and try to work out some sort of schedule,' " Shultz said.

Shultz's first trip to the Middle East as secretary of state comes six days after the bombing of the U.S. Embassy in Beirut in which 61 persons, including 17 Americans, were killed or are missing and presumed dead.

President Reagan said yesterday that the bombing, called by U.S. diplomats "the worst single blow the U.S. Foreign Service has ever received," strengthened his resolve to bring peace to the region.

At dusk yesterday, Reagan took what he called "one of the saddest journeys of my presidency," flying with Shultz by helicopter to Andrews Air Force Base for the arrival of a cargo plane carrying the flag-draped coffins of 16 Americans killed in the bombing. Relatives of the 17th victim had asked that he be buried in Lebanon.

"I undertake this task in great sadness but also with a tremendous sense of pride in those who sacrificed their lives in our country's efforts to bring peace to the Middle East and spare others the agony of war," Reagan said earlier in the day, in his weekly radio address. "Greater love hath no man."

The skies were gray, and a light rain was falling at Andrews when the camouflage-painted C141, carrying the coffins and an official delegation led by Undersecretary of State Lawrence S. Eagleburger, touched down after a 14-hour flight from Beirut.

Sixteen black hearses arrived at Andrews just before the plane. Also there, along with the president and his delegation, were family members and top Lebanese officials stationed in Washington. The somber ceremony was held in a hangar, instead of on the runway, because of the weather.

A military honor guard stood at attention in front of the caskets on a platform in the dank hangar, and a band played "The Battle Hymn of the Republic" as Reagan walked past.

The victims were "truly the peacemakers," he said. "They knew the road they traveled was hard and fraught with peril. They walked that road with cool professionalism and a deep sense of purpose."

Then, his tone changing, Reagan added: "Let us here in their presence serve notice to the cowardly, skulking barbarians in the world that they will not have their way."

In the interview Friday, Shultz said he does not agree with those who argue that Reagan's peace initiative, proposed Sept. 1, is dead.

"It seems to me that the desire, the need for peace, is not dead. It's very much alive. There's a yearning for it. Every event that happens only emphasizes its importance," he said.

"And, if that's your premise, then somewhere along the line you have to find your way to the parties in the region sitting down together and talking about it.

"Within that framework, you have to find your way to secure arrangements for Israel and some manner of recognizing the legitimate needs and aspirations of the Palestinian people. The president's plan does those things, and I think, therefore, that it must carry on. We expect to keep working on it," he said.

Shultz said the administration's effort to bring King Hussein into the Mideast talks on behalf of the Palestine Liberation Organization came close to succeeding before some PLO leaders rejected the idea.

Hussein met several times with PLO leader Yasser Arafat in an attempt to gain his support for participation in the talks but announced that he could not reach a satisfactory agreement.

"I do have the distinct feeling that King Hussein was ready to enter the peace process with the right kind of Palestinian delegation, and that at one point . . . he had the kind of arrangement with Arafat that would have permitted him to do that--permitted him in the sense that he wouldn't have been undercut by Palestinians or his fellow Arabs," Shultz said.

"It can't be called an agreement, because it didn't finally hold," Shultz added. "But, as I understand it, King Hussein and Mr. Arafat worked out an understanding of conditions that were acceptable to King Hussein and seemed to be reasonable, whereby King Hussein would enter the peace process, or make a statement that he was ready to do that, and that he would have a Palestinian delegation that consisted of legitimate Palestinian people who could claim to be genuinely representative, who were not members of the PLO."

Shultz said administration discussions with Hussein attempted to handle delicately the issue of Israel's continuing settlements on the West Bank, which the Arab leaders have said must stop before serious discussions can begin.

"What the president said to Hussein was, 'If you enter the negotiation, say you're ready to enter the negotiation. I will not press you to actually sit down at the bargaining table unless we find some form of freeze of the Israeli settlements ,' " Shultz said.

"Of course, King Hussein might decide to sit down anyway and say, 'The first thing I want to talk about is a settlement freeze.' But we haven't got to that point."