Prime Minister Menahem Begin today formally invited Egyptian President Anwar Sadat to visit Israel, and orders went out to officials at Ben Gurion Airport to take the red carpet out of storage.

The Israeli prime minister handed a larged white envelope containing the invitation to U.S. Ambassador Samuel Lewis, who promised that the American Embassy in Cairo would have it "within two or three hours."

The invitation was transmitted through the United States since Israel and Egypt have no diplomatic ties.

In Cairo, Sadat received U.S. Ambassador Hermann Eilts tonight. While the Egyptian government issued no immediate response to the invitation, Sadat emphasized earlier in the day that he had no intention of backing off from his offer become the first Arab leader ever to travel to the Jewish state to talk peace.

"I intend to go to the Israelis' den to tell them the truth," Sadat told a group of visiting U.S. congressmen. "I consider this trip as a sacred duty and this vicious circle we are turning around in . . . has to be broken."

While Sadat told the congreemen he would like to make the trip to Jerusalem "as quickly as possible," it appeared tonight that the historic meeting would not occur - if it does take place - at least until the end of next week.

Begin, who earlier had offered to postpone a scheduled weekend trip to London and Geneva if President Sadat wanted to fly to Israel that quickly, announced tonight that he will proceed with his travel plans.

Sources said he would be back in Jerusalem ready to receive the Egyptian President by next Thursday.

In Washington, the Carter administration, which until today had played no role in helping arrange what had been an almost unthinkable meeting, appeared to be dramatically revising upward its opinion of the event's importance.

Press secretary Jody Powell said the White House fully welcomes "this unprecendented exchange" between Israeli and Egyptian leaders.

At the same time, the U.S. reemphasized its desire to see the Geneva peace conference reconvened "as soon as possible."

"For our part, we will do anything necessary to facilitate contacts which we have always considered essentia if the parties to the dispute are to settle their differences themselves at the Geneva conference," State Department spokesman Hodding Carter daid.

Israeli officials walked around in something approaching a state of shock today with the realization that what seemingly started as a public relations gambit five days ago might actually result in an gyptian president coming to Jerusalem to address the Knesset.

"Yesterday, I was saying no. Today, I am not so sure," was the cautious response of one senior Israeli official. "We now see it as a realistic possibility," added another. "I don't see how he can really back away from it now."

Former Foreign Minister Yigal Alon agreed that Sadat now seemed committed" to coming.

Astonishingly, much of the Arab world also seemed resigned to the ideal of a Sadat visit to Israel actually taking place, although diplomatic sources in Damascus said Syrian President Hafez Assad planned to appeal to Sadat to change his mind when the two Arab leaders meet in the Syrian capital today.

What brought many officials both in Arab capitals and here in Israel to the belief that this extraordinary event might, in fact, actually occur was Sadat's dramatic interview with CBS news yesterday, in which he dropped any preconditions to his visit other than the desire to address the Knesset.

The possibility of a Begin-Sadat meeting also took on an added air of reality today when Israel formally asked the United States to transmit its invitation to Sadat, thus moving the event out of the realm of theater and into the world of diplomacy.

Until Begin handed the envelope to Ambassador Lewis, the entire exchange between the Israeli prime minister and Sadat, carried out through public pronouncements and television interviews, had struck some cynical observers as largely a media event.

Before transmitting the formal invitation to Sadat, Begin today first sought the approval of the Israeli Parliament.

During his presentation to the Knesset, Begin said he would also welcome visits to Israel by Syria's Assad, Jordan's King Hussein and Lebanon's President Elias Sarkis.

At that point, a member of the Knesset shouted out, "And the chairman of the PLO (Palestine Liberation Organization)."

Begin immediately brought the house down by declaring that he hoped the Communist members of Parliament would not interrupt Sadat when he was speaking.

"This invitation does not constitute any attempt to drive a wedge between the Arab states." Begin told the Knesset, "We are prepared to conduct negotiations for the achievement of peace in the Middle East and the signature of peace treaties with all our neighbors. With each and every one of them. I think it was only natural that I invited the president of Egypt. It is the largest of the Arab states. In our conviction, there is no basis for the conflict between Egypt and ourselves. The conflict has been tragic. Superfluous. Prolonged. And this is our appeal.

If Sadat does decide to visit Israel next week - or even in the near future - preparing for his arrival will pose a logistics and security nightmare.

"It's going to be sandlot football with Begin in the huddle saying you run that way and I'll pass because there isn't going to be much time to develop plays," said Zeev Chafets, head of the government press office. "At least when Nixon visited China, Kissinger had preceded him by two years and there was time to get ready."

Officials Ben Gurion Airport reported that they were getting the red carpet ready, but they did not have any Egyptian flags. They were hoping that the Foreign Ministry could supply them. "What about security?" asked Chafets. "There are hundreds of families who have lost their sons fighting the Egyptians. Some of them might be crazy?

"Somebody asked me if we could make arrangements of 2,000 newsmen and I said that's like asking Hadassah Hospital if they could make room for 200,000 casualties."

"There are simply no precedents for a thing like this," another official declared. "How do you make arrangements for a head of state of a country with whom you are technically at war?

Another question being asked here today was whether Egypt would send its own security people as an advance party to work with the Israeli security if Sadat accepted the invitation.

"You have to really hand it to Sadat," said an Israeli. "He really knows how to make an impact. Eisenhower won his election by saying he was going to Korea, but he didn't say he was going to North Korea - which is just about what Sadat is saying."

Gen. Mordechai Gur, chief of staff of the Israeli Army, poured water on the entire prospect by warning, in an interview with an Israeli paper, that the Egyptians might be preparing to attack Israel. But his boss, Defense Minister Ezer Weizman, quickly stated that he thought the general had exceeded his authority.

Gur warned that if Sadat was trying another deception similar to the Yom Kippur was in 1973, the Israelis knew what he was up to. Gur said that the Egyptians were making preparations that would allow them to make was against Israel in 1978, and that neither Israel nor the world should hold out hopes that could lead to "bitter disappointment or even worse."

A spokesman in Cairo was reported as saying that Gen. Gur had "no political understanding," which is exactly what a lot of people close to the prime minister of Israel were also saying tonight.

Israeli officials today were surprised at how there has been no adverse reaction from the Arab world to Sadat's proposal to visit Israel. They suggested, however, that the Arab world - like Israel - might be in a state of shock.

An Egyptian paper said today that the shock effect on Israel of the Sadat proposal was the same as the shock of the 1973 war, except that this time it was achieved by political instead of military means. Few Israelis would deny the truth of the statement.

Israelis grudgingly admitted that Sadat had created a "no lose" situation in which, if he failed to soften up the Israeli negotiating stance, he could say to the world: "Look, I have done my best." Sadat has made it clear that his trip is not to be a substitute for Geneva which, in Israel's view, increases the chances that he will actually decide to come.

"Sadat has always been a man of constant surprises," said one senior Israeli official today, "starting with his coming to power after Gamal Abdel Nasser's death. Not even our Mossad (secret service) predicted that."