Former presidents Jimmy Carter and Gerald R. Ford, old rivals who are nurturing a new friendship, found themselves in agreement on most major current issues as they co-chaired a public-policy seminar at the Ford Library here today.

They agreed on the need to reduce the projected federal budget deficits, on a stretch-out of defense spending and on recision of the indexation of income taxes.

The occasion was the inaugural conference of the Domestic Policy Association, a new network of colleges, libraries, museums and community groups that is trying to create a dialogue between the public and policy makers that emphasizes areas of common ground rather than dissent.

It attracted Cabinet-level officials from both men's administrations.

"Our relationship is a tribute to the American political system," Ford said in the kickoff of a day of Gerry-and-Jimmy bonhomie.

The program was not the first collaborative effort between Ford and Carter. They are co-authors of an article about the Middle East in the current Reader's Digest, and they will be together again at a seminar in Atlanta this fall commemorating the fifth anniversary of the signing of the Mideast peace accords at Camp David.

The friendship began when they flew to Egypt together last year for the funeral of Anwar Sadat.

Ford said it would be "catastrophic" if steps are not taken to reduce the government's huge budget deficits. He called for a stretch-out of Reagan's $1.6 trillion military buildup in which the funds would be spent over six years rather than the planned five. He also called for recision of the scheduled 1985 indexation of federal taxes to consumer prices, which is intended to prevent wage increases from exceeding inflation.

Carter echoed Ford's sentiments about the defense budget and the indexing, and advocated forgoing the third year of the Reagan tax cut, which is scheduled to take effect in July.

In a joint news conference, however, they took opposing views of the effects of the nuclear disarmament movement here and in Europe.

Ford said he fears that it will "handicap" American negotiators by encouraging the Soviets to believe they can "sit on the other side of the table and wait long enough" for public opinion in the West to force concessions.

Carter, who noted that the demonstrations did not begin until the Reagan administration took office, said he thought they had been beneficial in pushing along the negotiation process.

Carter also couldn't resist a few digs at the current administration when asked about Reagan's tendency to blame the economy's current woes on previous Democratic administrations.

"There is a natural temptation of any incumbent to blame his problems on his predecessors," Carter responded. "Most of us are able to resist that temptation. Some cannot. The longer you stay in office the less validity that kind of excuse has."

But most of the session had a lighter tone. Carter got the best laugh as he started to make a point about the continuity of the American political system.

"Presidents come and go," he began, then added, "sometimes all too frequently." Ford, standing next to him on the podium, laughed heartily and seconded the sentiment.

Both looked tanned and fit, though Ford was walking with crutches, a result of a recent operation on his left knee for a football injury here nearly 50 years ago.

The Domestic Policy Association was formed by David Mathews, president of the Kettering Foundation and secretary of the Department of Health, Education and Welfare in the Ford administration. Today's seminar followed a series of town meetings last fall at 145 sites in 17 states on Social Security, jobs and inflation.