The Reagan administration will seek to cut new federal loan obligations and loan guarantees proposed by former president Carter by $13.6 billion this year and $21 billion in 1982 as part of the detailed budget proposals it will send to Congress tomorrow.

The reductions in a host of government-backed lending programs, ranging from student loans to financing fast-food outlets through the Farmers Home Administration, would mean more freedom for financial markets to allocate credit and, as a result, lower interest rates, according to Office of Management and Budget Director David A. Stockman.

"Loan guarantees are basically not a business the government ought to be in," Stockman told reporters at an OMB briefing. "Every time you do it, you knock someone else out of the pew."

He was referring to the fact that, since there is only a given amount of money available in financial markets, whenever the government makes a direct loan or provides a loan guarantee, some other, less-creditworthy borrower gets squeezed out.

Most of the major lending or guarantee programs to be curtailed, such as those of the Export-Import Bank, the Rural Electrification Administration, the Economic Development Administration, the Federal Housing Administration and the Student Loan Marketing Association, were identified Feb. 18, when President Reagan made his first budget presentation to Congress.

But some further cuts are to be proposed tomorrow, and among the would-be borrowers on that list is the District of Columbia. Carter had recommended the D.C. government be allowed to borrow $133 million this year and $220 million in 1982 to finance a variety of capital improvements. Reagan has not changed this year's figure, but is expected to propose slashing the 1982 to $145 million.

Overall, the administration wants to limit new direct loan obligations for 1981 to $55 billion, down $2.6 billion from the Carter proposal, details of which have recently been revised by the OMB for technical accounting reasons. For 1982, such obligations would drop to $49,4 billion, also down $2.6 billion from the Carter total.

Loan guarantee commitments would be cut from Carter's proposed $96.2 billion this year to $85.2 billion. In 1981 such commitments would fall from Carter's $96.9 billion to $78.5 billion.

In direct loans, the Treasury or some other government agency lends money directly to the borrower. In the case of a loan guarantee, the borrower gets his money elsewhere -- from a bank, for example -- and government guarantees the loan will be repaid.

The proposals would have the greatest impact on middle-class Americans, the main beneficiaries of loans and guarantees the administration is attempting to cut. The Biggest reduction in loan guarantee authority, for example, would hit the Federal Housing Administration, which provides mortgage insurance for homebuyers.

The FHA would be allowed to insure only $34.4 billion worth of mortgages this year instead of the $39.2 billion recommended by Carter. Next year the cut would be deeper, to $35.4 billion from $44.3 billion.

Stockman said private mortgage insurance is available in most of the country to provide the same coverage, and the federal government need not be involved.

As for student loans, which would drop $1.4 billion in 1982 to $4.3 billion, Stockman said eligibility will be determined on basis of need, as is eligibility for grants.

Now anyone can apply for up to $2,500 a year, regardless of the income of the student or that of his family. Such guaranteed loans carry a 9 percent interest rate, with no interest charged until the student is out of school.

"I have run into people selling student loans along with oil-drilling tax shelters," Stockman said. "You get the loan, which is free money for four years, and invest it in the tax shelter. When the student graduates, you give him the shelter and he uses the income to pay off the loan."

Of the new so-called credit budget, Stockman said, "the significant thing is that we have taken a trend that was exploding upward at a $100 billion or $150 billion [annual] rate and actually reduced it."

Beryl Sprinkel, Treasury undersecretary for monetary affairs, said reduction in federal credit demands will contribute to the administration's objective of lowering both inflation and interest rates.