Treasury Secretary Donald T. Regan said yesterday that interest rates could rise further and remain high "for several months," possibly bringing on another "temporary" business slowdown this summer and autumn.

The secretary said the prime interest rate, which rose to 19 percent only last Monday, soon could jump to 20 percent. However, he asserted that although the high rates might make the economy "soggy," a recession is unlikely.

Regan also confirmed that the budget deficit this year now seems likely to approach $60 billion rather than the $54.9 billion expected previously -- mostly because of high interest rates and cost-of-living increases in social programs.

He said Director of Office of Management and Budget David A. Stockman is "looking everywhere" for between $2 billion and $5 billion in additional spending cuts to offset the higher deficit. But he offered no details on which programs might be cut.

In his remarks to reporters, the Treasury secretary conceded the rise in interest rates -- and the prospect of a slowdown later this year -- is "bitter medicine," but he said it is necessary to help combat inflation.

As have other officials before him, the Treasury secretary praised the Federal Reserve Board for having "got a handle" on the problem with its credit-tightening moves earlier this week, designed to rein the money supply.

Regan also raised the possibility that the administration, which pledged this year to keep its hands off the Social Security program, might propose changes for future years that would alter the system significantly.

Although officials haven't decided on any specifics, Regan listed as possibilities a change in cost-of-living adjustments, a tightening of eligibility for minimum benefits and a penalty for earlier retirement.

He also said the administration will have to decide whether in the longer run it wants to continue the program as an old-age pension or make Social Security merely a "backup" for those who can't obtain their own pension plan.

The Social Security program originally was intended as just such a "backup" plan when the system was put into effect in 1939. However, Congress gradually has expanded benefits far beyond the "subsistence."

He noted that some other nations encourage workers to enroll in private plans by providing substantial tax incentives for persons who save part of their earnings for their old age. The United States provides some tax incentives now.

Regan reiterated that although President Reagan promised not to touch Social Security this year, he "did not put himself in cement forever" on the issue. He said the commitment does not affect future budget plans.

The secretary's remarks confirmed the administration's willingness to accept the consequences of further credit-tightening by the Fed, which top Reagan economic advisers have been urging for the past several weeks.

Regan described the Fed's actions as "hitting the brakes a little harder." He also blamed the financial markets for "misinterpreting" the Fed's previous policies as being too lenient.

At the same time, the secretary again rejected suggestions that the administration trim back or delay its massive tax-cut package to help counter the swelling federal budget deficit.

Regan said the tax cut was needed to help offset the increased tax burdens that otherwise would result from the impact of inflation in pushing taxpayers into higher and higher brackets.

The secretary said the administration would use the same strategy on its tax-cut plan as it did on the Reagan budget cuts: "We're standing firm in our position. A lot of people came closer to what we want."

Regan's forecast of higher interest rates and a business slowdown was in line with that of both administration and private economists. He said the economy's output, adjusted for inflation, could decline slightly for a quarter.

However, the secretary dismissed as "on the high side" suggestions that the prime rate could soar as high as 24 percent or that interest rates will remain high for six months or more.

Regan conceded that he, along with many others, was surprised -- and a little apprehensive -- over the economy's rapid growth in the first quarter of this year. He said the fast pace implies that inflation pressures will remain in force.