President Carter led an all-out embrace yesterday of Egyptian President Anwar Sadat's projected visit to Israel, to dispel any impression of a grudging attitude toward the move, which caught his administration by surprise.

Carter called Sadat's decision "very courageous," "unprecedented" and "constructive." A State Department spokesman labeled it "imaginative, constructive and helpful." A senior official termed it "a historical psychological breakthrough."

At the same time, the President said, "no one knows what will happen," as "it's an unpredictable thing, but I believe it's a step in the right direction."

The administration, in sum, was elaborately revising its initial reaction of cautious skepticism that the Sadat offer was only a diamatic gesture. Its significance can be huge. U.S. officials now fully agree, but the diplomatic interaction is wholly unpredictable.

"Clearly this is a dynamic chance in the situation," State Department spokesman Hoding Carter III said yesterday.

In non-diplomatic terms, that means the entire administration, along with other nations, is now highly unsure what the impact will be on the nearly year-long U.S. push for a new Geneva conference on the Middle East. It would be composed of Israel, all its Arab war adversaries (Egypt, Syria, Jordan and Lebanon), Palestinian representatives still undefined and the United States and the Soviet Union.

The Carter administration put its prime emphasis on sustaining its Geneva conference diplomacy in the immediate wake of Israeli Prime Minister Begin's quick acceptance Monday of Sadat's specific offer to visit Israel. The Sadat initiative, while welcomed, must not be a substitute for Geneva, officials said.

That continues to be the basic U.S. diplomatic approach. Administration planners, however, do not want to appear to be denigrating the undisputed significance of a first-time visit of an Arab head of state to Israel.

Psychologically, administration officials see the implications of such a visit as profoundly beneficial - provided it does not backfire badly. Diplomatically, it is the equivalent of introducing a wild card into a poker game: it can change the value of everyone's hand, including Sadat's, in a manner which no one can predict.

This is "a high-risk undertaking," an authoritative administration official told reporters yesterday, speaking on a non-attribution basis.

Sadat, the U.S. official said, in presenting an all-Arab stand when he goes to Israel, runs the risk of overstating a hard position, and antagonizing the Israelis, to avoid being accused of undercutting militant Arab demands. Sadat in any event will call for total Israeli withdrawal from all war-won territory and creation of a Palestinian state, both roudnly opposed by Israel, Egyptian diplomats emphasize.

At the opposite pole, the U.S. official noted, Sadat has the risk of understating the all-Arab demands, in the search for compromise with Israel, and exposing himself to charges of a sellout from Arab militants.

If Sadat can surmount that double hazard, the American source said, then he could inject new life into the faltering drive for a reconvened Geneva conference.

There is also the chance, however, which Carter administration officials prefer not to focus on, that the American drive for a "comprehensive settlement" of the Arab-Israeli conflict will be overtaken by a move toward an Egyptian-Israeli settlement. Egyptian officials deny that is Sadat's intent.

Part of the uncertainty ahead, U.S. strategists hope, will be clarified by Sadat's important meeting yesterday with Syrian President Hafez Assad. Syria has been raising the largest objection to the intended format for a Geneva conference.

But there is also the strong possibility, administration official said yesrterday, that the Sadat-Assad outcome may be inconclusive. Assad could choose to wait to see if the Sadat mission founders in Israel.

President Carter, speaking to reporters yesterday after saying farwell to the shah of Iran, said he had not suggested to Sadat a visit to Israel. "No," he said, "that was President Sadat's idea."

"No one knows for sure what will occur if President Sadat goes to Jerusalem," Carter said, but "we have been pleased to see this develop."

"I've been in almost daily contact with President Sadat in the last coule of weeks," Carter said, "and have been glad to exchange messages between him and Prime Minister Begin."

Carter said it is his belief that Sadat will go to Israel, and, "I believe this will be a constructive step toward a general conference that will let the hopes for Middle Eastern peace come closer to realizatin. . ."

"This is an unprecedented thing, a very courageous thing, that President Sadat has proposed," Carter said. "As you know," he continued, "Israel and Egypt are technically at war, and no Arab leader so far as I know had ever before even recognized the legitimacy of the Israel government or the legitimacy of the knesset [parliament]."

"It's an unpredictable thing," however, the President repeated, "but I believe it's a step in the right direction."