The Senate Finance Committee agreed yesterday to reduce the "marriage penalty" on couples with two incomes, and voted to let employes put money aside in tax-sheltered Individual Retirement Accounts even if they are covered by pension plans where they work.

In all, nine assorted tax cuts were approved yesterday as the Republican-controlled Finance Committee neared completion of its work on a three-year bill that would cut personal and business taxes nearly $40 billion in fiscal 1982 and more than $240 billion in the following two years.

The committee approved new tax subsidies for research and development investments by business, tax cuts for Americans working abroad and tax credits for investments in used property and rehabilitated buildings.

An effort by Sen. Bill Bradley (D-N.J.) and a few liberal colleagues to change the Reagan administration's formula that the committee has also approved for across-the-board tax rate cuts for individual to tilt them more toward those earning less that $50,000 a year was easily rebuffed by committee Chairman Robert J. Dole (R-Kan).

"Let's give the president an opportunity to see if his plan will work," Dole told Bradley. "This is a tax program, not an [income] redistribution program."

But yesterday's steps forward on the Senate side were matched by a step back in the Democratic House, where feuding intensified between Treasury Secretary Donald T. Regan and Chairman Dan Rostenkowski (D-Ill.) of the Ways and Means Committee.

Rostenkowski sent Regan an acerbic letter denying that he and the majority Democrats on the committee were stalling on the tax bill, a charge Regan made on Monday in a speech to an American Stock Exchange symposium.

"The president's demand for a tax bill on his desk by Aug. 1 is high political theater at best. With business tax cuts, alone amounting to more than half a trillion dollars this decade, I believe that prudence -- rather than a media horse race -- would better serve the nation's taxpayers," Rostenkowski said.

Saying that he expects to have a tax bill through the House in July, he added, "I hope over time you will learn the details of the process by which we must all work."

The Ways and Means Committee -- chastised by Regan for working "three-hour days" -- took no action yesterday, but its members indicated that they are prepared to support the new kind of savings certificate approved by the Senate Finance Committee on Monday as a crutch for hard-hit-savings and loan institutions and the housing industry.

The Senate measure, opposed by the administration, would create savings certificates paying 70 percent of the interest rate on one-year Treasury bills.A single taxpayer could receive up to $1,000 in a tax-free interest from the certificates in a year, and couples filing a joint return up to $2,000.

Backers of the certificate plan say it would provide a critical flow of savings into thrift institutions, several hundred of which are close to bankruptcy because they can't match the interest rates offered by banks and the money market.

On Monday, the Finance Committee's Republican majority defeated Democratic attempts to earmark the certificates for savings and loan institutions rather than banks, many of which are enjoying record profits.

Yesterday, Senate Democrats tried to regain the initiative with a caucus resolution calling on the administration to recognize the critical plight of the thrift institutions.

There is no argument in Congress about reducing the "marriage penalty" in present tax law that generally imposes a higher tax on a married couple with two incomes than the two would face if single and earning the same amounts.

The Senate committee's change would permit the spouse with the lower earned income to take a special deduction on the couple's joint return, of 5 percent to a maximum of $1,500 in 1982 and 10 percent to a maximum of $3,000 thereafter.

The proposal would wipe out about half of the current marriage penalty at a cost to the Treasury of $7 billion a year.

In broadening the rules for IRAs, the committee voted to permit participants in company-sponsored retirement plans to make tax-free investments of up to $1,000 in their own individual retirement funds.

The committee also voted an increase, from $5,500 to $2,000, in the top limit on tax-free IRA investments by employes not participating in company-sponsored pension plans.

In a related change, the committee agreed to raise the maximum tax-deductible contribution that self-employed taxpayers can make to retirement plans, from the current $7,500 to $15,000.

To encourage U.S. companies to employ more Americans abroad, the committee voted to make as much as $75,000 of foreign-earned income tax free each year. The committee also agreed to reduce taxes on stock options granted by companies to attract key executives.