Rep. Richard A. Gephardt (D-Mo.) said yesterday that Congress should seek an agreement with the White House for a tax increase to help avoid drastic spending cuts next year under the new Gramm-Rudman-Hollings budget-balancing law.

In remarks to a legislative strategy session of the American Association of Retired Persons and in an interview later, Gephardt said he would prefer to raise income taxes. But he said Congress is more likely to support an increase in gasoline taxes or oil import fees if petroleum prices continue to fall.

Gephardt, chairman of the House Democratic Caucus, acknowledged that President Reagan has indicated no softening of his opposition to a tax increase and conceded that a tax increase "isn't going to happen" without Reagan's support.

But Gephardt's advocacy on the eve of Congress' return today underscores mounting pressure on Capitol Hill for a tax increase to minimize damage to domestic and defense programs under the new law, designed to force a balanced budget by fiscal 1991.

Mandatory cuts of $11.7 billion for the rest of fiscal 1986 are scheduled to take effect March 1. Anticipated cuts approaching $60 billion for fiscal 1987 will take effect Oct. 15 unless Congress and Reagan agree on an alternative.

In a separate assessment, Rep. Charles E. Schumer (D-N.Y.) said yesterday that the legislation will require cuts next year of nearly 28 percent in a wide variety of social programs, along with a reduction of nearly 17 percent in defense spending. Cumulative cuts for the two years would amount to 31 percent for domestic programs and 21 percent for defense, he said.

Defense and domestic spending will be cut equally in dollar terms, but the domestic percentage is higher because many programs, including Social Security and antipoverty spending, are exempt.

Schumer opposed the budget-balancing law when it was enacted late last year, calling it "self-inflicted fiscal terrorism" and predicting that it would be repealed or substantially revised when its full impact became clear.

For the first two years, Schumer calculates a reduction in student loans from $4.9 billion to $3.4 billion; housing for the elderly and handicapped from $1.9 billion to $1.3 billion; the National Institutes of Health from $5.5 billion to $3.8 billion; the Federal Bureau of Investigation from $1.2 billion to $843 million, and the Internal Revenue Service from $3.6 billion to $2.5 billion.

Schumer said in an interview that he also would favor a tax increase but added, "Gramm-Rudman has to be repealed, first and foremost." Even with a tax increase, he said, "it would be impossible to reach $144 billion the deficit target for fiscal 1987 without serious damage to the economy."

But Gephardt, while characterizing the Gramm-Rudman-Hollings law as a "blunt instrument," said he hoped it will help bring Congress and the White House to the bargaining table after five years of budget stalemate.

He said he thinks that the House-passed tax-overhaul legislation pending in the Senate might be the proper vehicle for a tax increase. But he said such an increase could be considered separately.

Spending will have to be cut to persuade Reagan and members of Congress to agree to a tax increase, Gephardt said. But to require massive deficit reductions through spending cuts alone, as the president is expected to do in his fiscal 1987 budget, is "wrong-headed," he said.