President Anwar Sadat accepted the invitation to the Camp David Summit seconds after Secretary of State Cyrus Vance extended it to him without asking for any assurances of new Israeli concessions, a senior state department official said last night.

The immediate acceptance surprised Vance, who had expected the Egyptian leader to ask for time to consider the American effort to get peace talks started again, the official said.

Israeli Prime Minister Menachem Begin also agreed to the Camp David meeting.

American officials declined to discuss the substance of the talks with Sadat, but the fact that he accepted it before hearing anything else Vance had to say suggested that the Egyptian leader was eager to find a way now to keep alive the peace progress he set in motion eight months ago.

Great secrecy surrounded the delivering of the handwritten notes from President Carter inviting the two leaders to Camp David. Neither had been told before hand that Vance was bringing the invitation.

The Soviet Union was not advised in advance of the move, nor were any of Sadat's Arab allies, who have been increasingly nervous about the failure of his initiative to produce Israeli concessions.

At a press conference following their second night of talks here, Sadat and Vance ducked all questions about what would be discussed at the Camp David meeting and declined to speculate on the prospects for its success. The overall impression they left was that Sadat's faltering peace initiative has been kept alive by an eleventh-hour American intervention, but that a long road still lies ahead to the peace that all sides say they seek.

During the brief press conference, however, Vance agreed with Sadat's characterization of the American role in the upcoming talks as that of a full partner.

In that context, the secretary said that the United Sates would be ready to offer proposals of its own to the two sides if that would help overcome specific obstacles.

"We seek the same objective" of a lasting peace Vance said in explaining the U.S. willingness to be a full partner. But the secretary was careful not to specify the objectives of U.S. hopes to achieve with the conference.

Sadat has frequently asked the United States to become a full partner by presenting an American peace plan, hoping such a plan would be favorable to the Arabs.

Vance's remarks may thus help the Egyptian leader in climbing down from the position he has been taking since last month's foreign ministerial-level talks at Leeds Castle in Britain failed to produce any progress toward peace.

He has insisted since then that he would not agree to any more direct negotiations with Israel unless there was some indication in advance that the Israeli position was softening.

He also let it be known through unofficial channels that he did not wish personally to have any more dealings with Israeli Prime Minister Menachem Begin.

Sadat is now going into new talks with Begin on just the terms he had pronounced unacceptable.

Asked why, Sadat suggested yesterday that the personal invitation from Carter was the key factor.

"After I have read the personal message that was delivered to me, I have decided to go to Camp David for the purpose that was announced, to seek a framework for peace," he said.

That was the same formulation he uses last month when he made clear, in accepting an invitation from Vice President Walter Mondale to send his foreign minister to the talks in Britain, that he was doing so only at the behest of the Americans.

This time the difference, aside from the level at which the meeting will be conducted, is that the United States is moving more directly into the negotiations, assuring the Egyptians that U.N. Security council Resolution 242 must be the basis of any settlement.

Since the United States has repeatedly said that it interprets the resolution to require Israeli withdrawal on all fronts from Arab territories occupied in 1967, Vance's words are in line with what the Egyptians want to hear.

Egyptain Officials stressed that there has been consideration of temporary or partial solutions such as an extension of the second Sinai disengagement agreement.

They said it continues to be Egypt's position that there must be a comprehensive regional agreement because nothing else will work, and that the United States had agreed. This is an important point for the Egyptians because it bolsters what remain of their hope to induce Jordan and eventually Syria to enter the talks.

If any concessions are to be made on the West Bank from the Arab side, they can't be made by us. It has to be by the Palestinians, an authoritative Egyptian official said.

Stressing that time was important, Vance said the decision to invite Begin and Sadat to Camp David had been taken "to move the peace process back on the track."

Sadat, who is customarily forthcoming at press conferences, was unusually reticent last night.

Asked what would happen if the talks failed to produce any results, which is a distinct possibility, Sadat said he would "cross that bridge when we come to it."

In a way, The Sadat initiative itself is now over and a new phase has begun. Sadat himself said the Camp David talks will open a "new page in the negotiations. Let us not look back," he said.

Sadat and Vance met for two hours last night, long after it had already been officially announced in Washington that the Camp David proposal had been accepted by both Israel and Egypt.

The U.S. ambassador to Saudi Arabia, John West, who was here during the discussions, departs for Saudi Arabia to convey the news to the government in Riyadh.