President Reagan said today that the nation's economic recovery has begun, and cited an expanding Chrysler auto plant he toured near here as part of the evidence that America "is on the comeback trail."

"Economic recovery is something like a seedling," Reagan told about 800 auto workers at the Chrysler plant in suburban Fenton. "For a while, it goes underground and you don't see it above ground, and then it shoots up and seeds are sprouting all over the place. And that's what we're starting to see around the nation right now: the shoots of an economic recovery are beginning to push up through the recession with attending unemployment."

After touring the plant with Chrysler's president, Lee A. Iacocca, and Missouri's Republican governor, Christopher S. Bond, Reagan told a group of St. Louis businessmen that, "We are beginning to receive the payoff we have all been waiting for--the reward for painful but essential steps to cure a disease [inflation] that was crippling America and undermining our security."

Reagan said evidence of the recovery includes increasing auto sales, rising housing starts, higher wages after inflation and record levels of investments in small businesses. He added that new unemployment claims also are declining.

The Chrysler plant that Reagan toured in a golf cart, followed by three Dodge trucks filled with reporters and photographers, is undergoing a $96 million expansion to more than double its output and create 1,400 to 1,700 jobs, according to the auto company. The plant, which was shut in 1980, leaving 4,000 workers without jobs, is producing 1984 model cars.

In speaking to the auto workers, Reagan did not mention the $1.5 billion federal loan guarantee to Chrysler that brought the company back from the brink of default. Reagan originally had opposed the loan, but said as a presidential candidate in May, 1980, that while he "opposed the loan in principle" he would support help for Chrysler. He has since stated his opposition to further assistance for struggling firms.

The president told St. Louis businessmen that he remains committed to his tax policies despite pressure to cancel the third year of income tax cuts, scheduled to take effect in July, and to do away with future adjusting of tax brackets to inflation.

Attacking Democratic critics of the budget he sent to Congress Monday, Reagan said, "Rather than bringing spending down close to revenues, they simply raise revenues the sneaky way by using inflation to push every working family in America toward higher and higher tax brackets. Ironically, they call that program compassionate and fair."

He added that opponents who want to do away with the tax cuts and tax indexing would "destroy the incentive to reduce projected deficits and will instead sabotage recovery and make deficits worse. So, again, we in government must take the lead of a genuine recovery budget."

Reagan also sought to correct the record on the only passage in his State of the Union address last week to draw a standing ovation, led by Democrats in Congress.

"There seems to be a little confusion about a sentence I used in my State of the Union speech last week," the president said. " . . . That we in government must take the lead in restoring the economy. Some people seem to think that I was advocating a return to the old ways. I didn't mean anything of the kind.

"I meant, government was largely responsible for creating the economic mess of recent years; now it must recognize that and start undoing the damage it has done."

In an interview with The St. Louis Post-Dispatch on his flight here, Reagan said he expected economic recovery to be more robust than the estimates of his own advisors. He said they have been "conservative in their predictions of a modest recovery through the end of 1983."

In response to a plea from a businessman from suburban Times Beach for help in coping with recent flood damage and contamination by the chemical dioxin, the president agreed to add a Times Beach resident to a federal task force formed to deal with the problems.

Times Beach contractor Laine Jumper was among those in the audience of St. Louis-area businessmen who asked Reagan questions after his speech today. Jumper called Times Beach "the single most depressed area of small business in the United States of America." CAPTION: Picture, Reagan, with Missouri Gov. Bond tours a Chrysler auto plant at St. Louis, where a $96 million expansion program is expected to create up to 1,700 jobs. AP