Prime Minister Menachem Begin said today that Israel faces new and serious danger as a result of U.S. Senate approval of the $8.5 billion arms sale to Saudi Arabia and pledged that the Israeli government will take steps to "overcome" the threat posed by the sale.

Begin did not spell out in the official Cabinet statement what Israel will do to counteract what it sees as the new threat, but he pointedly noted that President Reagan had reassured him that the United States will help Israel retain its "military and technological advantages."

Cabinet sources said some ministers at today's session complained that the statement, drafted by Begin, was not strong enough.

Defense Minister Ariel Sharon, who did not attend the Cabinet meeting, later issued a toughly worded statement saying the Senate action is "unusually serious" and will reduce Israel's strategic advantage over the Saudis and other Arab countries as well.

Sharon said it is "well-known" that Saudi Arabia transfers arms purchases to other countries, and he repeated his charge that Saudi-bound arms from the United States are being transferred to Iraq.

Begin's oblique reference to counteracting the sale to Saudi Arabia of sophisticated radar surveillance aircraft and range-extending equipment for F15 warplanes suggested the likelihood of new Israeli requests for U.S. military assistance to compensate for what Israel views as a loss in military superiority resulting from the Saudi arms deal.

Aides to Begin would not discuss the specifics of what he meant, but when asked if it involves a trade-off of military aid, one official replied, "Not exactly in those terms. It's more in the area of the strategic cooperation discussions and in general the United States commitment to Israel."

He added, "It's not a quid pro quo, like so many tanks and planes for the AWACS. It's not a bookkeeping matter of give-and-take. It's a whole setup of understandings between the United States and Israel."

Following an emergency meeting of his Cabinet, Begin said the Israeli government "expresses its regret" over the Senate vote allowing Reagan to sell the planes and arms to Saudi Arabia, which, Begin said, "is in a state of war with Israel, rejects the Camp David accords and finances terror in the region."

Begin said the national-security danger posed to Israel by the sale is unique in the 33-year history of the Jewish state, adding, "We will have to overcome this threat also. We will do all that we have to do in order to overcome it."

Begin said he received a letter this morning from Reagan, dated yesterday, in which Reagan promised to help Israel retain its military superiority in the Middle East.

In the letter, Reagan said: "The security of Israel remains an essential factor in our decisions on strategic issues in the region. This administration has a continued interest in working with Israel on a wide dimension of strategic issues, efforts which serve our mutual interests."

After reading Reagan's letter, Begin told reporters: "We hope that these words of the president will be carried into realization."

Looking somber and refusing to answer questions, Begin said that during the long Saudi arms debate, "friends of Israel, regardless of the origin or political affiliation, conducted a just struggle with courage and dignity."

Among those who supported the arms sale, Begin said, are "many who value the role and policy of Israel in the Middle East and in the free world and nurture in their hearts warm feelings toward our people and country."

Condemnation of the Senate vote came from a broad political spectrum of members of Israel's parliament, with Communications Minister Mordechai Zippori of the rightist Herut faction of Begin's Likud bloc and Victor Shemtov of the leftist Mapam faction of the opposition Labor Alignment using similar language against the sale.

Both said that the arms deal poses a dual danger: to Israel because of the enhanced strike capability they contend the Saudis will achieve, and to the United States because of the instability of Saudi Arabia and the likelihood that the Airborne Warning and Control System (AWACS) aircraft could come into the hands of other countries hostile to Israel.

Opposition leader Shimon Peres charged that the sale will alter the strategic balance in the Middle East and pose a major threat to Israel's security.

Meanwhile, U.S. Jewish leaders here for an international conference of the United Israel Appeal called on the United States to balance the Saudi deal by maintaining Israel's military superiority in the region.

Maynard Wishner, president of the American Jewish Congress, also contended that the Jewish community in the United States came out of the losing vote stronger than before.

"I don't remember an issue in which the Jewish community was better organized, more responsive, more united, more coordinated in its thinking and its processes and how it carried on this effort," Wishner said.