The Senate leadership buckled under pressure from the banking industry yesterday and agreed to defer withholding of taxes on dividend and interest income until at least 1987 and perhaps forever.

The Senate was expected to agree easily to the deferral, and a majority of the House also opposes the provision, which Congress enacted only last year. But the House leadership and President Reagan favor withholding, and Reagan has vowed to veto any bill repealing it.

Whether withholding will take effect as scheduled July 1 was thus unclear last night. But the Senate leadership's capitulation "means that we have made the possibility of withholding very remote," said freshman Sen. Robert W. Kasten Jr. (R-Wis.), the leading opponent of withholding.

Kasten, who had just forced Sen. Robert J. Dole (R-Kan.), chairman of the Finance Committee, to accept almost complete defeat, said, "I don't think the president is going to have a lot of choice" in deciding whether to accept the deal.

"Very frankly, we didn't have the votes," Dole said afterward on the Senate floor.

Jerry Lowrie, chief lobbyist for the American Bankers Association said, "We are encouraged by the reported developments, which appear to meet the principal concerns expressed by the American public. We are anxiously awaiting tomorrow's actions and believe that the elements now exist for a solution acceptable by all."

The banking industry has lobbied intensely for months to have withholding repealed.

Under yesterday's "compromise:"

* The 10 percent withholding of taxes on dividend and interest income which was to have started July 1 would be postponed at least until July, 1987.

* Until then taxpayers would have to include with their returns so-called 1099 forms, which list dividend and interest income just as the more familiar W-2 forms list wages. The Internal Revenue Service would use these in checking returns, and new penalties would apply to those who failed to report interest and dividend income.

* The General Accounting Office (GAO) would then study 1985 tax data to determine whether taxpayers still were not reporting all dividend and interest income. If it turned out that taxpayers were reporting less than 95 percent, and both House and Senate took affirmative votes, withholding would start in July, 1987. But such votes seem unlikely, given the opposition the banks were able to drum up so easliy this winter.

Kasten said the GAO provisions were intended to give Reagan "some wiggle room" so that he could describe the deal as a compromise.

The withholding provision would raise an estimated $13.4 billion from 1983 through 1988, mostly through payment of taxes on income that now goes unreported. Dividend and interest income goes disproportionately to taxpayers in the upper income brackets.

Similar proposals had been rejected consistently by Congress in the past. It was enacted last year as part of a set of tax increases, all of which were considered essential in the effort to reduce federal deficits.

The Kasten-Dole agreement, if it goes as planned, is to be added to a trade bill now on the Senate floor.

The Internal Revenue Service estimates that only 89 percent of interest income and 85 percent of dividend income was reported, with unpaid tax of more than $8 billion.