Israel's decision to turn down President Carter's invitation to a peace summit is likely to reinforce the Egyptian view that the Israelis cannot be trusted. According to Prime Minister Mustapha Khalil, it was Israeli Foreign Minister Moshe Dayan who proposed the meeting in the first place.

Khalil, reached by telephone after his return from negotiations in Washington, said Dayan told him it would be necessary to call Prime Minister Menachem Begin to participate in the negotiations because Dayan was not authorized to make substantive decisions. Therefore, Khalil said, he and Dayan jointly drafted the letter of invitation that Carter read out two days later.

The refusal of the Israeli Cabinet to authorize Begin to participate in a meeting proposed by their own foreign minister, Khalil said, was "not Egypt's problem."

Khalil is to report to President Anwar Sadat on Wednesday. Sadat, who is in Alexandria, Egypt, has not commented directly. But he authorized an "official source" to say that because of the instability of the Middle East, the United States "cannot allow the situation to remain fluid -- and will have to put pressure on Israel."

The comment came before the latenight news that Begin had accepted Carter's request for an urgent meeting in Washington, which seemed to fall in line with Egyptian thinking that the next move is up to Carter.

In the Egyptian view, the outcome of the Israeli Cabinet meeting was a vindication of Sadat's decision not to go to Camp David himself. Egyptian sources said Sadat declined to take part because he was unwilling to put himself in a situation where he could make binding commitments under pressure from Carter while Begin still had an escape hatch -- his need for approval by his Cabinet or parliament of any binding peace formula.

"With Khalil having full authority, we can't be the ones accused of backing down," a Foreign Ministry official said. "Our view was that when the Israelis are ready to deal on a final basis, Sadat will go along."

Until the announcement from Israel this afternoon, the Egyptians apparently believed that progress was being made.

On arrival at Cairo airport. Khalil told reporters, "In my view, real progress has been achieved." But he said there was "no agreement."

Later, he said that he and Dayan, together with Secretary of State Cyrus Vance, had worked through seven different formulations of a letter that is a key to the proposed treaty -- clearly the one dealing with Palestinian autonomy, although he would not say so -- without reaching complete agreement on it.

He said it was "not true" that Egypt had "hardened" its position during last week's talks, as the Israelis charged in turning down the summit conference invitation.

According to Egyptian sources, Sadat and Khalil feel they are now in a good tactical position: they have negotiated and are willing to keep on negotiating, and are still willing to go to take part in the Camp David talks, while they have not yet given up anything that would bring down the further wrath of other Arabs. Nor can Sadat be blamed for refusing to go to Camp David, since he was not actually invited, they said.

But these public relations successes do not actually bring closer to hand the treaty to which Sadat has said he is committed.

According to Egyptian officials, Sadat is increasingly uncomfortable at having gone so far in definace of other Arab leaders only to come up short. They believe Sadat is now sincere in saying that he canot yield any more on the remaining substantive points, but the longer the impasse goes on, the more delicate his position becomes.