Former president Carter, in a move that put him at odds with many Democratic Party leaders, yesterday endorsed President Reagan's proposal to sell sophisticated radar planes and other advanced aircraft equipment to Saudi Arabia.

In a letter to Sen. Sam Nunn (D-Ga.), Carter allied himself with the Reagan administration's intense lobbying effort to block a possible congressional veto of the $8.5 billion sale. He asked Nunn "to share my views with other members of the Senate" and said:

"For the well-being of our own country, for the continuing security of Israel, and for the peace and security in the Middle East and Persian Gulf area, I hope that you and other members of the Senate will give him [Reagan] this support."

White House strategists have sought Carter's endorsement in hopes it will swing some undecided votes, particularly among Senate Democrats, in favor of the sale. However, opponents of the deal, pointing out that 32 Democratic senators already are on record as opposing the sale, have predicted that Carter's backing will have little or no effect on an expected heavy Democratic vote against the deal when the Senate considers it Oct. 20.

The endorsement came as no surprise. Senior officials of Carter's administration have admitted publicly that a decision in principle was made late last year -- when Carter was still in office -- to sell the Saudis such radar surveillance planes as the Airborne Warning and Control System (AWACS) planes that are the main items in Reagan's proposed package.

These same officials, among them former defense secretary Harold Brown and former secretary of state Edmund S. Muskie, also have said Carter planned to sell the Saudis other items included in the impending sale such as range-extending fuel tanks for the F15 jet fighter-bombers whose sale to Saudi Arabia Carter arranged in 1978.

In fact, the Carter administration told Reagan's people during the transition period that it was willing to take responsibility for officially consummating the sale. Reagan refused the offer, but his administration subsequently decided it would go ahead with the deal and include five AWACS planes as well.

Carter's position put him on the opposite side of the AWACS controversy from the Democratic National Committee and most of the party's other leading figures.

The executive committee of the Democratic National Committee passed a resolution during the summer condemning the sale; the party chairman, Charles T. Manatt, has been instrumental in organizing an anti-AWACS coalition, headed by J. C. Turner, president of the International Union of Operating Engineers, and former Republican senator Clifford P. Case of New Jersey.

Carter's statement disconcerted some of his longtime supporters. Lynn Cutler of Iowa, national vice chairman of the DNC and sponsor of the anti-AWACS resolution, said it was "unfortunate" that the former president had split from the party on "the first significant issue that he's spoken to where we have been deeply involved."

Former vice president Mondale told the New York Daily News last spring that "selling AWACS planes to Saudi Arabia is the wrong decision done in the wrong way at the wrong time."

That same stand, essentially, has been taken by Sen. Edward M. Kennedy (D-Mass.) and most of the other 1984 Democratic presidential aspirants in the Senate. They also differ publicly with the view Carter expressed Saturday that the United States must talk with the Palestine Liberation Organization to advance Mideast peace.

Carter and former president Ford enunciated that position to reporters while flying back to the United States from Cairo, where they attended the funeral of Anwar Sadat.

In his letter, Carter said he had "always found the Saudi Arabian leaders to be staunch friends of our country" and added that carrying through with the sale "has become a litmus test of America's reliability."

Conceding "the Saudis and other Arabs have not supported the Camp David peace process as much as we would have liked," he insisted: "The Saudis are not a warlike people and greatly desire peace and stability."