Voter support for President Reagan has increased sharply in recent weeks despite widespread discontent with many specific aspects of his handling of the presidency, according to a new Washington Post-ABC News public opinion poll.

Reagan has drawn even or slightly ahead of the two leading contenders for the Democratic nomination in 1984, after trailing them since January. Among registered voters, Reagan now edges former vice president Walter F. Mondale by 46 to 45 percent and Sen. John Glenn (D-Ohio) by 44 to 43 percent, according to the poll taken April 8 through 12.

As recently as early March, Mondale led Reagan by 49 to 40, and Glenn led by 48 to 38 among registered voters.

Reagan's sudden advance coincides with strong suggestions from the president's top two aides that he will decide to seek a second term.

Presidential counselor Edwin Meese III told reporters yesterday that if Reagan "had to make the decision today he would definitely plan to run" and circumstances are unlikely to change by the time he decides this summer. White House chief of staff James A. Baker III said in Houston Wednesday that an announcement Reagan makes after Labor Day will "gladden the hearts of his admirers around the country."

Two factors appear to be tied to Reagan's sudden increase in support in The Post-ABC News poll: a perception that he deserves credit for what many Americans see as an improvement in the economy, and the failure of the Democrats so far to capitalize on his weaknesses.

For the second month in a row, almost four of every 10 people in The Post-ABC News poll said they feel the nation's economy is getting better. That is a striking change from a dozen earlier polls, in which no more than 21 percent saw the economy improving.

But Reagan was unable in early March to make any political gain from this rosier outlook, according to The Post-ABC News poll. In an attempt to change that, the Republican National Committee spent $1 million to broadcast a television commercial in mid-March in 45 of the nation's more than 200 TV markets.

It showed a working-class housewife in her kitchen saying, "Some of my friends think President Reagan was just too doggone optimistic. He figured he'd get the economy moving a lot faster than he's been able to." The woman then said that "people are going back to work because President Reagan didn't go for a quick fix. Maybe we can be a little more optimistic about the future."

Reagan's pollster, Richard Wirthlin, said in a telephone interview yesterday that his new poll shows Reagan with a sharply higher approval rating in those 45 markets than elsewhere. He also said people in areas where the ad was shown are more optimistic about the economy than are other Americans.

Whether due to that TV commercial or not, The Post-ABC News poll shows that the Republicans message appears to be getting across to the one group among whom it can do the most good: independent voters.

In March, registered independents split almost evenly for Reagan and the two Democrats. In the new Post-ABC News poll they favored Reagan by 53 to 36 percent over Mondale, and by 49 to 37 percent over Glenn.

Overall, however, the public is sharply critical of Reagan. A majority said he should not run for president, that the nation continues to be off on the wrong track under his stewardship, that he is doing poorly at handling the economy (despite the perceived turnaround), at handling inflation and unemployment.

Reagan gets negative ratings, in fact, on all nine questions dealing with particular aspects of his presidency, ranging from the economy to his handling of the Social Security System, cuts in social programs and foreign affairs. By 2 to 1, citizens interviewed say his presidency has made things worse rather than better for people where they live.

Asked whether they prefer Reagan's requested 10 percent increase in military spending for 1984 or plans offered by House Democrats to increase the military budget by less than half that amount, only 32 percent of those interviewed support the president.

Fifty-five percent say the Democrats' proposal "is closer to what we should be spending," and an additional 6 percent say there should either be no increase or a decrease in military spending.

The public also lines up strongly against Reagan by giving overwhelming support to proposals for a nuclear freeze. While the president has charged that encouragement of a freeze works against nuclear arms reduction, 8 in 10 in the new poll said they approve of a freeze by the United States and the Soviet Union.

In addition, many citizens--3 in 10 of those polled--express concern that Reagan's policies are increasing the chances for nuclear war, while only half that number see Reagan's policies as reducing the threat of nuclear war.

The public is split and apparently confused on Reagan's call for development of laser and particle beam systems in space aimed at guarding against nuclear attack. By 54 to 37, a majority favors developing such defensive weapons.

But in a response to a follow-up question, by 57 to 24 percent, citizens feel development of such weapons would lead to an increase rather than a decrease of the arms race between the United States and the Soviet Union.

Despite Reagan's negative ratings on most questions, he shows some improvement in the standard question dealing with presidential popularity.

In March, 45 percent said they approved his handling of the presidency and 50 percent said they disapproved, with 5 percent expressing no opinion. In the new poll, 49 percent say they approve, 47 percent say they disapprove, and 4 percent offer no opinion.

On another issue, the poll found the public sharply divided over newly enacted changes in the Social Security system. The changes, recommended by a bipartisan commission appointed by Reagan and now awaiting the president's signature, have been hailed as proof the parties, working together, can solve difficult national problems.

In the poll, however, only one-third say they feel the changes will keep the Social Security system out of financial trouble.