Despite a vigorous lobbying campaign by bankers last week, President Reagan said yesterday that he has not changed his mind about the new tax law requiring 10 percent withholding on interest and dividends from savings accounts and that he will veto any congressional attempt to repeal it.

Three groups of bankers, homebuilders and real estate men visited Reagan at the White House last week as part of one of the most intense lobbying drives in recent years. They asked the president to reconsider his support for the withholding provision of the 1982 tax bill scheduled to take effect July 1.

Supporters of the repeal argue that 75 percent of taxpayers have enough withheld from their wages to cover their entire tax liability and that the new law would penalize retirees but not stop tax cheating since banks are required to accept all tax-exemption requests.

Reagan contends that the law will recoup $18 billion over the next five years in tax revenue that otherwise would be lost to tax cheaters."Thanks to the pressure from a very busy lobby," he said yesterday in his weekly radio address, "the Congress is now considering repeal of withholding before it's even gone into effect . . . . It would let all those who are not paying their taxes on interest and dividends off the hook.

"So I'm not about to let that happen . . . . I'm carrying my veto pen right behind my ear. If the repeal passes the Congress, I'm all set to veto it just as I am prepared to protect the July tax cut and indexing with a veto if necessary."

The lobbying campaign led House Minority Leader Robert H. Michel (R-Ill.) to join in opposition to the provision.

Late last month, Rep. Dick Cheney (R-Wyo.), head of the House Republican Policy Committee and a Reagan political ally, said GOP members of Congress feel almost unanimously that the president and Republicans should abandon the bill because it is "creating a hell of a problem" for the party.

Cheney predicted that a veto of any repeal measure would be overridden in Congress.

A key test vote is scheduled in the Senate Tuesday on closing debate on the withholding provision to allow a vote. There are thought to be enough votes to repeal the provision in the House and Senate, but it is not known if there are enough to override a veto.

Rep. Norman E. D'Amours (D-N.H.), a member of the Banking, Finance and Urban Affairs Committee and author of the House petition to repeal the law, issued a statement after the president spoke and said:

"Why penalize the overwhelming majority of honest taxpayers to get a at a few tax cheats when we have a better way to accomplish the same goal by better enforcement of existing laws although the president, Treasury Secretary Donald T. Regan and Sen. Robert J. Dole Finance Committee chairman refuse to acknowledge this point . . . . "

Dole (R-Kan.) said after the president's speech that he still has the support of House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.). Rostenkowski has refused to allow a bill to stop the law out of his committee.