Senate and House conferees yesterday broke a week-long impasse and reached agreement on a bill to repeal the 10 percent withholding of taxes on dividend and interest income that was to have gone into effect July 1.

The breakthrough came a day after the Treasury Department, which twice had postponed enforcement of withholding in anticipation of repeal by Congress, said it would not grant further delay beyond Aug. 5, when Congress is scheduled to recess for a month.

Majorities in both chambers favor repeal, and congressional leaders said there would be no difficulty in securing passage of the legislation before the Labor Day recess.

President Reagan opposes the repeal of withholding taxes on dividend and interest income, but he has said he will sign the bill because the conferees attached to it legislation granting tax and tariff benefits for 28 friendly Caribbean nations that the administration proposed as part of its Caribbean Basin Initiative. The Caribbean Basin plan, which the administration describes as a constructive balance to its more controversial military moves in Central America, would permit many items manufactured in the region to be imported into the United States duty free for 12 years, and would extend some tax incentives to business development in the region.

The impasse by House and Senate conferees was broken when Sen. Lloyd Bentsen (D-Tex.) agreed to drop an unrelated measure that had been attached to the repeal bill by the Senate Finance Committee.

Withholding of dividend and interest income at the source was one of the key tax-compliance provisions of the 1982 tax act. It was expected to increase federal revenues by $13.4 billion over the next three years by enabling the Internal Revenue Service to collect taxes on income that had been going unreported.

But withholding was strongly opposed by the banking lobby, which engineered an avalance of mail from taxpayers who apparently were convinced that it represented an additional tax on their savings and investments. So intense was the pressure that both chambers overrode the chairmen of the House Ways and Means Committee and the Senate Finance Committee--the tax-writing committees--and voted for repeal.

In an effort to limit the revenue-reducing impact of repeal, the conferees accepted a Senate-sponsored package of enforcement and compliance procedures that could recover more than $4 billion of the $13.4 billion.

One would allow the IRS to impose "backup withholding" at a rate of 20 percent on taxpayers who fail to report all dividend and interest income. Another would provide at least $300 million a year for the IRS to hire additional personnel to identify delinquents.