The Reagan administration yesterday laid out proposals to increase taxes by $86.6 billion through 1987 and to include the withholding of taxes for the first time from dividend and interest payments.

The withholding would be 5 percent. Similar proposals have been shot down by the banking lobby at least twice in the past.

Most of the other revenue-raising ideas also are guaranteed to produce opposition in this election year from such influential interest groups as defense contractors, state and local governments and the insurance industry.

On Capitol Hill, where many GOP senators and House members were pressing for much larger tax increases to reduce the likely deficit, the Reagan proposals met with at best a lukewarm reception.

Senate Finance Committee Chairman Robert J. Dole (R-Kan.) warned that "if in three months there is no sign of things getting better" Congress may have to press President Reagan to propose significant new tax increases. "I don't want to raise taxes, but I do want to reduce the deficit," Dole said.

Under the withholding plan, banks, savings and loans and corporations would be required to turn over to the Treasury 5 percent of all interest and dividend payments, except for those to recipients qualifying for exemption. Among these would be elderly couples making $14,907 or less in 1983.

The Treasury says that 9 to 16 percent of taxable interest and dividend income is not reported. The revenue from this shift would be $2 billion in 1983, $1.3 billion in 1984 and $1.9 billion by 1987, according to the Treasury.

Within minutes after the announcement of the withholding plan the U.S. League of Savings Association issued a statement denouncing it as "an unnecessary and unfair scheme which has twice been rejected by the Congress and the American people."

Another controversial proposal by the administration is to set a minimum corporate income tax on firms that pay very low taxes.

This minimum tax would apply to income shielded from the regular income tax by preferences in the code.

Among the preferences the administration is expected to include are some leasing provisions, under which companies can now buy and sell tax breaks, the investment tax credit, the use of domestic international sales corporations, the right to expense or deduct all at once intangible drilling costs on oil wells, percentage depletion, maritime subsidies, motor carrier operating subsidies and interest on loans used to buy tax-exempt bonds.

Every industry that currently benefits from these tax preferences is sure to put up a major fight to get exempted from the list. These include multinationals, banks, oil companies, shipbuilders and truckers.

Dole is likely to try to expand the minimum tax proposal to include wealthy individuals who pay very low tax rates.

Equally explosive is an administration plan to end by regulation what is known as the completed contract rule. Under the rule companies with long-term contracts, particularly defense contractors, can postpone income tax liability until the contract is completed.

The administration changes would require companies to pay taxes on the basis of the percentage of the contract completed each year or on the basis of the progress payments that are received.

Other revenue-raising proposals include accelerating the rate at which corporations must pay taxes, a step that would produce $1.4 billion in 1983, and beefing up the enforcement staff of the Internal Revenue Service, a step Treasury claims would produce $2.1 billion in 1983 alone.

Treasury Secretary Donald T. Regan also disclosed that Reagan wants to hire 5,000 more Internal Revenue Service agents, including auditors and debt collectors, to help bring in more revenue. Regan said the government would raise $4 for each $1 it spends to hire agents.