Like a nagging reminder of what lies ahead, the subject of presidential politics in general, and of Sen. Edward M. Kennedy (D-Mass.) in particular, was thrown up repeatedly yesterday to a reluctant President Carter.

The president was holding his first nationally televised news conference in Washington since July 25, in the course of which he deplored the tendency to begin presidential election campaigning earlier and earlier every four years.

"I don't think it is in the best interests of our country to start so early," Carter said.

But amid questions about Soviet military strength, tight-money policies of the Federal Reserve Board and mass starvation in Cambodia, the dialogue returned repeatedly to the 1980 campaign and the almost certain challenge the president faces from Kennedy for the Democratic presdential nomination.

How does he think he will do Saturday in the nonbinding Democratic caucuses in Florida, widely viewed as the first test of strength between the White House and supporters of Kennedy?

"This is one of the evidences of an increasingly early attention focused on a presidential race," Carter replied, quickly skirting over the enormous effort in money and manpower his campaign committee is investing in the Florida test. "It will be significant, but I cannot predict the outcome of the caucuses."

Did he think that Kennedy's behavior in the 1969 Chappaquiddick accident -- in which a young woman in Kennedy's car drowned -- would be an issue, and had he meant to raise that subject during a "town meeting" two weeks ago in Queens, N.Y.?

"I did not refer to Sen. Kennedy's experience at Chappaquiddick in Queens, and I have no desire to comment on it now," the president replied, cutting off further inquiries on the subject.

Would he be willing to debate Kenedy during the primary campaign, and if he is denied the nomination will he support the Democratic nominee against his Republican challenger?

"That's a lot of conjecture," Carter said, finally answering under further questioning that "my presumption is that I would support whatever Democrat gets the nomination."

Much has happened since Carter last held a news conference. Andrew Young resigned as United Nations ambassador; Soviet troops in Cuba became a major issue, imperiling Senate approval of the strategic arms limitation treaty; the economy weakened as inflation continued unabated, and the price of gold set records on world markets.

Many of these subjects were raised yesterday, but none more than the other intervening event -- Kennedy's "signals" that he intends to challenge Carter next year over the economy and the president's leadership.

Paraphrasing a speech Kennedy gave two weeks ago in Boston, Judy Woodruff of NBC asked Carter:

"Sen. Kennedy has suggested that, instead of complaining about what I believe you call the malaise the country is experiencing, that what the president should do now is ask the people to roll up their sleeves to try to pull the country out of its problems and in effect he spoke of a can-do spirit that harkens back to the 1960s."

"Is this a campaign speech for him?" A smiling Carter interjected.

The president then gave his repsonse, touching on what could be a major theme if the contest between him and Kennedy remains centered on the question of "leadership."

Obviously there is a degree of malaise in the country," he said. "People are discouraged about their current situation. They are doubtful about the future . . . "

But Carter added, "I said our country is inherently strong, capable and able, that there is no need for us to be discouraged or disillusioned or divided or doubtful about one another or about our government processes."

The test in dealing with this "malaise," the president said, will be in enacting a national energy program. "I am not discouraged," he declared. "I believe that we can succeed."

Throughout the news conference, Carter appeared reluctant to discuss presidential politics. At one point he suggested that he will announce his reelection plans on Dec. 4 largely because "there is a limit to how late one can wait."

He also reiterated that Vice President Mondale will be his running mate. Recent suggestions that the First Lady is becoming too visible as his trusted adviser he dismissed as a case of the press only now "paying attention to where my wife goes and what she says."

The news conference also demonstrated that even reporters are not immune to a slip of the tongue when it comes to discussing the Kennedy family. Pat Sloyan of Newsday, the Long Island newspaper, asked Carter: "Do you think that Chappaquiddick indicates that President Kennedy's character is somewhat flawed . . . ?"

"I think it is Sen. Kennedy," the president replied.