Egyptian President Anwar Sadat said yesterday that he is seriously prepared to go to Israel within a week if he receives a formal invitation from Prime Minister Menahem Begin.

"Very good news," the Israeli prime minister declared later in the day. Begin said he would ask the United States to relay a formal invitation to Sadat today, and even offered to postpone a scheduled visit to Britain next week so he would be on hand to welcome Sadat to Jerusalem.

"Any time, any day he is prepared to come, I will receive him cordially at the airport, go together with him to Jerusalem, also present him to the Knesset and let him make a speech to our parliament," Begin said. "It is now up to President Sadat to carry out his promise and bring it to fruition."

Sadat's offer - more explicit than anything he has said before about a willingness to go to Israel to talk peace - and Begin's reply were made in interviews with CBS correspondent Walter Cronkite, via satellite.

The Sadat-begin exchanges seemed at the outset to be a public relations initiative by Sadat, but they have turned into a potentially sensational development in the Middle East - if a visit materializes. That is a major qualification.

Sadat, in the CBS interview last night, insisted: "I'm just waiting for the proper invitation." Asked how soon he would be prepared to go to Israel, Sadat said, "At the earliest time possible."

When asked if he meant "within a week," the Egyptian leader replied, "You can say that, yes."

He said "my responsibility as president of Egypt . . . is to try all means to reach peace." Sadat said he wants to tell "the 120 members of the Knesset" the "situation from our point of view," and is prepared for an "exchange of views" with Begin.

Sadat said he had not discussed his idea with other Arab leaders, and conceded that "for sure, there are those who are against it." But, the Egyptian president added: "I am convinced that this is the right way - and my people back me . . ."

Begin said he will make a statement today in Parliament about his invitation to Sadat, and then will consult with U.S. Ambassador to Israel Samuel W. Lewis about transmitting the invitation.

The formal invitation would be sent through the United States because Israel and Egypt, which have fought four wars in 29 years, have no diplomatic relations.

Begin said he felt that British Prime Minister James Callaghan would be ready to postpone his scheduled talks with Begin "for a week and [would] rather have President Sadat in Jerusalem."

The State Department said earlier in the day, before the latest Sadat offer, that "we welcome all statements and gestures" that contibute to movement toward a Geneva peace confederence. That is where the official U.S. focus has been.

The Sadat-begin exchange, which Sadat initiated last Wednesday, had been regarded as important atmospherics, but hardly the core of diplomacy.

American officials have been anxiously looking to Sadat's meeting with Syrian President Hafez Assad, on Wednesday to determine if Egypt's drive for Arab flexibility in launching peace talks with Israel can be sustained.

Sadat's attempt to overcome the procedural obstacles to a Geneva peace conference, an effort explicitly endorsed by President Carter, will be at stake in that Damascus meeting.

Also at stake will be months of American diplomacy to produce the conference, which is now virtually beyond reach by December. The issue now is how to keep the momentum going to assemble the conference in January or early February, and one option is a new round of talks by Secretary of State Cyrus R. Vance.

If diplomatic conditions warrant, administration officials said yesterday, Vance would hold a new round of "proximity talks" with Israeli and Arab foreign ministers in Europe in early December, perhaps in Paris.

These talks, similar to Vance's September-October discussions with the same ministers at the United Nations, would be added to his scheduled trip to Brussels for the Dec. 7-8 NATO meeting.

Two weeks ago, when Cairo reports said Sadat had suggested to Vance new Arab-israeli "proximity talks", administration officials discounted the report. U.S. officials said yesterday, however, that this has been "a recurring idea," and is now considered "a live option". There are still "no plans at this point" for such a trip. State Department spokesman Hodding Carter III said.

A double set of tentative developments have added new sparks of hope to the flagging prospects for a Geneva conference, administration sources said.

The weekend Arab conference of foreign ministers in Tunis lent itself to Egypt's strategy by avoiding rigid positions that could foreclose compromise on terms for reconvening the Geneva conference.

So, apparently, did the Palestine Liberation Orgainization, at Tun's, although with greater ambiguity.

By calling Sunday for the United Nations to invite "representatives of the Palestinian people" to Geneva in behalf of the conference cosponsors, the United States and the Soviet Union, the PLO appeared to be leaving a path open for diplomatic maneuvering. Israel will accept "Palestinians" at Geneva, but not official PLO representatives.

A PLO spokesman also said, however, that the Oct. 1 American-Soviet declaration, recognizing the "legitimate rights" of the Palestinian people, must be considered to be an official document fo the U.N. Security Council, and the basis for a peace ocnference.

Israel has rejected any obligation to the U.S.-Soviet statement, which it opposed. The State Department reiterated yesterday that the US.-Soviet statement is not a required basis for a Geneva conference, as it has assured Israel.

Last weekend, Sadat publicly floated the idea he privately submitted earlier to President Carter to have the Palestinians represented at Geneva by an American university professor.

State Department spokesman Carter confirmed yesterday that the President had received the proposal. An administration source said the significance of that Sadat proposal is that it stimulates the idea that "there are alternatives to the PLO" to represent the Palestinians, and the representatives need not be extremists.

Similarly, administration sources said Sadat's offer to go to Israel has more long-term implications than mere "posturing." That applies equally to Begin's response, it was said.

"In the bad old days," said one U.S. source, "Sadat would have been denounced as a traitor tot he Arab cause" for such an overture. Whatever the outcome, as of now the Sadat-Begin exchange, "has removed the stigma, or taboo, on the Arab side of having any contact with Israel. This is an important contribution," this source noted.