A special Reagan administration envoy met with Egypt's foreign minister today in an effort to smooth over relations deeply strained since the interception of an official Egyptian plane carrying the hijackers of the cruise ship Achille Lauro.

A U.S. Embassy official described the mood as "upbeat" at the 75-minute meeting between U.S. Deputy Secretary of State John C. Whitehead and Egyptian Foreign Minister Esmat Abdel-Meguid, and a subsequent lunch that included President Hosni Mubarak's top national security adviser.

Whitehead delivered a message on "recent developments in the area" to Abdel-Meguid from Secretary of State George P. Shultz, a Foreign Ministry spokesman said.

Whitehead is to meet Monday with Mubarak, who charged in a CBS-TV "60 Minutes" interview taped here Saturday that Tunisia and the United States jointly tricked Egypt into sending the plane carrying the Achille Lauro hijackers to Tunis so that it could be intercepted by U.S. Navy jets.

Mubarak also told CBS that he had tried to send the hijackers to another, unnamed country, but ordered them brought back when he found that "there was no responsible man of the PLO to receive them" there.

[He called the U.S. interception of the Egyptian plane "a stab in the back . . . from a friend," but said he understood that "if we were in your position also, we will not apologize." Mubarak suggested, however, that "There are several forms for apology."]

Egypt is the second stop on Whitehead's three-nation fence-mending mission, which began in Rome yesterday and will continue in Tunisia, where normally cordial relations with the United States were undermined by President Reagan's initial unconditional backing for Israel's raid on the headquarters of the Palestine Liberation Organization outside Tunis on Oct. 1.

Whitehead's visit here comes as both Cairo and Washington find themselves hard pressed to renew their formerly warm and mutually vital ties at the same time that they seek to satisfy the demands of national pride and their domestic constituencies.

The question of an apology is the essential stumbling block.

Mubarak maintains that Egyptian sovereignty was violated by the American interception of the plane and passengers whose safety he had guaranteed to end the cruise ship hijacking.

Reagan has refused to apologize because the United States considered its action necessary to bring the hijackers to justice for the slaying of 69-year-old Leon Klinghoffer.

"What are you asking us to apologize for?" one U.S. official demanded privately prior to Whitehead's arrival. But he also suggested a diplomatic maneuver around the impasse.

If the answer is "for arresting the hijackers," the American response will be "never," this official said.

"But if you are asking the Americans to say they understand" the feelings of Mubarak and the people here, then clearly "we're not happy that they are feeling so angry and so bruised," the official said.

U.S. Ambassador Nicholas Veliotes issued a public statement last week in an attempt to begin this process of diminishing the differences. One U.S. official called the Whitehead visit "a gesture on the public, political, psychological front."

But the signs from Mubarak remain, for the moment, unenthusiastic.

While Whitehead was meeting with Abdel-Meguid and both men lunched with national security adviser Osama Baz, Mubarak appeared to be playing a game of diplomatic diffidence.

The Egyptian president spent the day cutting a ribbon on a new poultry processing plant and laying a cornerstone for a planned city at Beni Suef, about 70 miles south of the capital.

"The American envoy knew before he left the United States that I would meet with him on Monday," Mubarak told reporters there. "He knew perfectly well that I was busy on Saturday and Sunday. And this should not be interpreted that I left him waiting for a while."

But this morning's semiofficial newspapers, aimed at a domestic audience, made a point of saying that Mubarak would be away during the first day of Whitehead's visit.

Anti-American sentiment appears to be running higher here than at any time in a decade.

At least two violent demonstrations denouncing the United States have rocked Cairo's university since the plane interception, only to be broken up by police charges and tear gas. Many Americans have been warned by their employers and by schools to be cautious on the streets.

Meanwhile, neither Mubarak nor the semiofficial press has accepted key points in the U.S. case against the Palestinians.

As late as yesterday, the major government-supported newspapers were suggesting that the hijackers' victim may not have been murdered because "no bullets were found in Klinghoffer's body."

Egypt, when it decided to intervene in the hijacking of the Italian cruise ship, asked representatives of the PLO to handle the negotiations.

The man the PLO chose was Mohammed Abbas, head of the faction of the splinter group Palestine Liberation Front whose men took over the ship after it left the Egyptian port of Alexandria. The United States has accused Abbas of conceiving and ordering the hijacking operation.

Today Mubarak was quoted by Information Minister Safwat Sharif as telling officials of his party in Beni Suef that "Egypt has no proof that Abbas played any role in the hijacking of the Italian ship."

Sharif also said that Mubarak acknowledged having requested Italy not to hold Abbas after the plane was intercepted.

U.S. officials expressed outrage when the Palestinian leader was allowed to leave Italy for Yugoslavia within 48 hours of the plane's landing. Italian officials have said that the United States failed to present sufficient evidence to detain Abbas under provisions of Italian law.

In the "Sixty Minutes" interview with CBS' Diane Sawyer, Mubarak said:

*"We asked permission for Egyptair [the government-chartered plane carrying the hijackers] lined up to go to Tunisia . . . . They asked the Americans. The Americans told them, 'give them permission.' At that time you decided to take the decision for the interception . . . . You knew the information through Tunisia, and we are sure of that."

*Abbas was in Cairo for a one-day stop at the time of the hijacking. "We found him by chance here. So our people here asked him to come and help. And frankly, we didn't realize all what was said by the Americans or by the Israelis about Abu Abbas."

*Had PLO leader Yasser Arafat put the hijackers on trial, it would have been "much better. We will avoid much more terrorism at least. We will avoid retaliation."

*Reagan is "a hero now because he intercepted our jetliner. . . . I'm very pleased that this interception of the jetliner raised the morale of the Americans. It's very good. We did something for you."