Treasury Secretary Donald T. Regan agreed yesterday to postpone for a month the withholding of taxes on interest and dividend income scheduled to begin July 1.

His decision was an acknowledgment that Congress will almost certainly repeal the withholding provision over the objections of President Reagan and many of its own leaders.

The announcement came as the Senate passed a bill to drop withholding, which Congress passed only last year, but at the same time increase surveillance of tax returns with dividend and interest income and stiffen penalties for failure to report such funds. Regan said he was putting off the withholding effective date only on condition these stepped-up compliance provisions were adopted; they are intended to salvage some of the revenue withholding would bring in.

The Senate also attached to its bill several other tax initiatives of the administration, including special tax cuts for businesses that move into deteriorating "enterprise zones" in major cities and tax and tariff portions of the president's plan to shore up the economy of the Caribbean Basin.

All these provisions may make for a difficult conference with the House on the withholding issue. House Democrats want Republicans to choose between the banking industry, which has led the fight to kill withholding, and the president, who has supported it; they have approved a simple bill to repeal withholding and do nothing more.

The withholding action came as, on another issue, the House Ways and Means Committee approved a bill to limit the income tax cut scheduled for this July to a maximum of $720 per return.

The vote was 18 to 15, with four Democrats joining the Republicans in opposition, calling into question the likely outcome on the House floor. There will also be opposition in the Senate to any cap on the tax cut, and Reagan has threatened to veto a capping bill.

House Democratic leaders have proposed a cap as a way of reducing next year's deficit and increasing tax fairness--only those in the upper income brackets would be affected--but they lack the votes to override a veto.

The Ways and Means Democrats who voted against the cap were Reps. Sam Gibbons (Fla.), Marty Russo (Ill.), Wyche Fowler Jr. (Ga.) and Thomas J. Downey (N.Y.).

The $720 cap would raise only about $6 billion next year. Resisting Democrats see relatively little fiscal gain in this, but great political risk; they fear Reagan will use it to brand them again as the party of higher taxes and spending.

In the Senate, Democrats fought but failed to strip the enterprise zone, Caribbean Basin and other provisions from the withholding bill.

The most important such stripping amendment, by Sen. Russell B. Long (D-La.), senior Democrat on the Finance Committee, lost 51 to 46.

Urged on by Finance Chairman Robert J. Dole (R-Kan.), the Senate then passed the bill 86 to 4.

As finally approved, the withholding bill includes an expanded system of reporting dividends and interest and a backup set of penalties that will require withholding of delinquent taxpayers' payments in the future. It also includes provisions expanding presidential authority to act in international trade disputes.

Another provision would eliminate the Dec. 31 expiration date for tax-exempt mortgage revenue bonds issued by local governments. These bonds, which are intended to provide mortgage money for home buyers who cannot afford market interest rates, will no longer be exempt from federal taxation unless the expiration date is repealed.

Many payers of interest and dividends had already made preparations for the 10 percent withholding that had been scheduled to start in two weeks. Presumably they will now all put these plans in abeyance, but that remained unclear last night.