Almost six in 10 Americans feel Ronald Reagan should not run for a second term as president, according to a new Washington Post-ABC News poll.

If Reagan were to run again, he would be trailing if the Democratic candidate were Edward Kennedy but leading if it were Walter Mondale, as things now stand.

The poll did not ask citizens why they were opposed to Reagan's seeking reelection, but the pattern of responses made it clear that those who have been most dissatisfied with his presidency are the ones who want him to step down in favor of another Republican nominee in 1984.

Ninety-five percent of blacks who were interviewed, for example, said Reagan should not run again. Among Democrats, 81 percent said the president should not seek reelection.

But opposition also surfaces in segments of the electorate that helped elect Reagan. Independent voters, a key to his victory over Jimmy Carter in 1980, now oppose a second Reagan candidacy by 50 to 42 percent, with 8 percent expressing no opinion. Even one-third of the Republicans interviewed said they are opposed to Reagan's seeking renomination.

In all, 35 percent of those who said they voted for Reagan in 1980 -- and 58 percent of all those polled -- said he should not seek re-election. Only 37 percent of all those polled said he should run again.

In the trial heat against Kennedy, the Massachusetts Democrat currently leads by 48 to 39 percent. Pitted against Mondale, however, Reagan is ahead by 45 to 38 percent.

In both instances, Reagan bests his opponent among men -- by a very narrow margin against Kennedy but substantially against Mondale. Among women, however, Kennedy holds a 19-point lead over Reagan -- 53 to 34 -- while Mondale leads the president by 3 points, 41 to 38.

Reagan has done poorly among women in virtually all polls since he began running for president. This so-called "gender gap" has been one of the most discussed political phenomena of the past year.

But Kennedy also has had problems of the same kind, doing considerably worse among women than men in his bid for the Democratic nomination in the 1980 primaries. Mondale has had no such difficulty, and it is therefore striking that Kennedy does so much better among women than the former vice president does in trial heats against Reagan.

One suggestion is that, through his struggles in the 1980 campaign, Kennedy has finally put Chappaquiddick behind him among large numbers of women. But only another run for the presidency, not a between-years poll, could really determine that.

Another possibility, however, seems to fit both the strong support for Kennedy and the weak showing of Reagan: women have not accepted the Reagan dictum that the domestic programs of the past 30 years have been failures. In most polls, women tend to be far more opposed than men to military spending and more in favor of social programs. And in recent years, Kennedy, perhaps more than any other Democrat, has been an outspoken defender of such liberal programs.

The "gender gap," in this view, may be tied more to traditional liberal-conservative politics than to any other factors.

In other matters, the new Post-ABC News poll, which was conducted by telephone from Sept. 9 through Sept. 13, found that:

Reagan's overall approval rating is holding steady, with 48 percent saying they approve his handling of the presidency and 45 percent disapproving, virtually no change from the 49-to-47 rating in a mid-August Post-ABC news poll.

Despite passage of a new tax bill and claims that economic recovery is at hand, the public continues to take a dim view, with 21 percent saying the economy is getting better, 45 percent saying it is getting worse and 33 percent saying it is staying about the same.

Only 47 percent say they have "heard or read" anything of the president's new plan for Palestinians, which would give autonomy to Palestinians on the West Bank of the Jordan River under some link with the government of Jordan. Among those familiar with the plan, citizens are sharply divided, with 44 percent favoring it and 37 percent opposed.

In all, 1,505 people nationwide were interviewed in the poll.