WASHINGTON--President Reagan vetoed a major trade bill for the second time in three years yesterday, and the House swiftly countered by voting to enact the measure over his objections.

"I am convinced this bill will cost jobs and damage our economic growth," Reagan said in focusing his veto message on a provision that would require companies to give their employees notice of plant closings and large-scale layoffs.

Within hours, the House voted, 308-113, to override the veto. The margin was well above the two-thirds majority required, but it was thought unlikely that the Senate would go along when it considers the override after the Memorial Day recess.

Sixty House Republicans defected from the administration and voted to override. Only one Democrat, Robert Mrazek of New York, a strong advocate of free trade, voted to sustain the president.

Lawmakers said Reagan's action represented the launching of a major campaign issue.

"I happen to think it's a better issue for the Democrats than for the Republicans," said House Speaker Jim Wright (D-Tex.). House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) asked, "Why hand it to us on a silver platter?"

Democratic presidential front-runner Michael Dukakis wasted no time seizing it. He called the veto "unconscionable."

Dukakis said Reagan and Vice President George Bush "don't understand that for working families who struggle to pay the mortgage, save for their children's education and care for their elders, there is nothing more painful than losing a job."

"Any administration that is willing to give General [Manuel] Noriega 120 days notice and a plea bargain ought to be willing to give the American worker 60 days notice before they are thrown out on the street," Dukakis said. He referred to a tentative deal to drop drug charges against the Panamanian strongman if he agrees to relinquish power and leave Panama by August.

Senate Majority Leader Robert Byrd (D-W.Va.) acknowledged that the Senate would not override the president when it considers the veto early next month, but he scoffed at Reagan's request for speedy consideration of a stripped-down version of the bill.

In particular, Reagan objected to the plant-closing requirement, as well as provisions restricting the export of Alaskan oil. White House spokesman Marlin Fitzwater said the president would sign a new bill that deleted both sections.

But Byrd warned that it will be "extremely difficult" for a new bill to wend its way through the chamber's complex procedures before its Oct. 8 adjournment. "Anybody who thinks that can be done in the Senate is simply naive," he said.

Wright, speaking with reporters before Reagan acted, said that if Democrats can't override Reagan's veto, they would push "the strongest, most effective trade bill that you can, but that will take time."

Senate Republican Leader Bob Dole of Kansas predicted, however, that not only would the veto be sustained in the Senate, but a cleaner version will become law.

"There's enough time. If the House sends us a trade bill and says `Take it or leave it,' I think we'll take it," he said.