Thirteen nations have fallen more than $28 million behind in interest payments to the United States for arms purchases, including three countries that the Reagan administration has selected for sizable new loans to buy more U.S. military equipment, according to a study by the General Accounting Office.

GAO, an auditing arm of Congress, warned that more defaults are likely at a time the Pentagon fund set up to cover them is dwindling. Liabilities under the program have increased from $12 billion to $18 billion in two years, and the Pentagon's reserve fund now holds less than $900 million.

Critics say the guaranteed loan program is merely putting off an expensive day of reckoning when U.S. taxpayers' money finally will have to be used to pay back the military debts run up by America's arms customers.

The loan program, which has become instrumental in keeping U.S. weapons flowing to developing countries, was set up in the mid-1970s by a Congress under fire for big budget deficits and lavish foreign aid programs.

The program relieved Congress of the political problems of appropriating military aid in the federal budget. Instead, the U.S. Treasury provided the arms-buying credits, the Pentagon guaranteed the loans and the foreign customers paid the going commercial interest rate.

But in the wake of skyrocketing interest rates and growing financial problems in Third World countries, serious doubts have begun to be raised about many countries' ability to pay their military creditors in the Pentagon if the current pace of arms deliveries continues.

GAO and other sources cite a number of reasons for concern:

The number of countries falling behind on payments, and technically in default, has been on the rise, from two in 1978 to 13 as of mid-February. Some officials predict that waiving payments, already permitted for Israel and Egypt, is destined to become a major and costly part of future military aid worldwide.

The Pentagon reserve fund that covers defaults has declined from a peak of $1.17 billion in 1980 to $860 million now, although liabilities under the guaranteed loan program increased from $12 billion to $18 billion in the same period. "With additional defaults likely, the fund is probably already overextended," the GAO report said.

Egypt and Israel, which received half of the $3 billion in guaranteed loans distributed in 1982, are strained by the growing military debt to the United States. Some officials say there is "no way" they will be able to keep up with their payments at their present rate of procurement without new American aid.

If interest rates remain at 13 1/2 percent during this decade, Egypt will be paying $1.2 billion a year by 1989 in interest alone on old American military loans, according to government estimates. Israel, which is facing principal and interest payments of almost $20 billion over the next 30 years, is already paying $910 million a year to keep up.

Under a special system called cash-flow financing, Egypt has been able to buy "much more U.S. equipment than would ordinarily be possible" but without any assurances that the government will supply additional aid in the future to pay for the extra materiel, according to GAO.

Turkey, Peru, Liberia and Zaire have arranged, or are attempting to arrange, a postponement of military debt to the Pentagon totaling $428 million. But some officials question whether these countries will be able to repay the loans even if the payments are rescheduled.

U.S. weapons sales made possible by the guaranteed loans have been important to American arms manufacturers, the armed services and U.S. diplomacy. They have helped lower the cost to the U.S. military of new weapons systems, such as the F16 air combat fighter, provided a commercial entry into new markets in the Third World for American multinational corporations, and helped the State Department and Pentagon win friends and gain favors abroad.

The problem is that the growth markets for foreign military sales today are not industrial countries, as they were after World War II, but developing countries that are facing unprecedented financial difficulties.

Most of the guaranteed loans are for 30 years, with a 10-year "grace" period during which the arms customer pays only the interest. But the interest payments quickly become substantial burdens for countries that already are having difficulties paying their foreign debts.

As long as there is some money in the Pentagon's reserve fund, defaults can be covered without getting new funds from Congress. This reserve has been used to cover defaults by 13 countries: Bolivia, Nicaragua, Ethiopia, Costa Rica, El Salvador, Liberia, Senegal, Tunisia, Zaire, Lebanon, Morocco, Sudan and Turkey, the last three of which are earmarked by the administration for more loans. But when and if this money runs out, as some fear could happen quickly if Egypt and Israel are unable to keep up, Congress will have to appropriate more funds to replenish it.

Anticipating these problems, Sen. Alan Cranston (D-Calif.) has proposed a formula in which the U.S. government would guarantee Israel enough additional aid so Washington would be assured of being paid back. The proposal, which some critics said would be like a bank loaning creditors money to pay the bank back, was applauded by several Senate Democrats but denounced by Republicans who said it was an open-ended commitment that would escalate aid to Israel and encourage other countries to ask for the same treatment.

Sen. William Proxmire (D-Wis.), who commissioned the recent GAO study on military assistance programs, has warned that "action is needed to rein in the proliferation of military aid programs and hold them to account."

Officials acknowledge that the guaranteed loan program lacks a formal procedure for assessing the creditworthiness of the countries receiving the loans.

"I don't believe there are any requirements that the president or anyone find a country creditworthy before extending a loan guarantee," said Peter Mackey, manager of the Treasury's Federal Financing Bank, which handles the guaranteed military aid loans.

"If the Department of Defense comes to us and says it will guarantee a loan, there's no reason for us to say no," said Mackey, whose bank has a full-time staff of seven.

At the same time, officials said they have only scanty information about the impact that growing military debts of dozens of developing countries is likely to have on their ability to deal with pressing social and economic problems.

Behind these difficulties is a history of changing American military aid policy.

From the end of World War II until 1975, the backbone of this aid was the military assistance program, or MAP. MAP dispensed $53 billion in military equipment and technical assistance to friendly countries, including $14.7 billion to South Vietnam.

This changed as Congress responded to growing public resentment at budget deficits and disillusionment with military sales in the wake of the Indochinese war.

The new mainstay of military aid became the guaranteed loan program, for which Congress has appropriated no money since one month after the 1980 November election, when funding of the Pentagon reserve that backs the program was ended. Since 1976 nearly $18.9 billion has been loaned out, according to GAO.

Responding to the financial problems of hard-pressed military aid recipients, the Reagan administration tried in its first year in office to lighten the load caused by weapons purchases. The administration asked Congress to increase appropriations for military grants and low-interest credits, while holding down the guaranteed loan program. But a cost-conscious Congress rejected this and insisted that guaranteed loans, dispensed at market rates of interest, continue as the main form of military aid.

In the case of Turkey and Sudan, which in this fiscal year received $343 million and $75 million in guaranteed loans respectively, "the increased levels of guaranteed credits at market rates will cause these two countries to have extreme problems making payments," according to a GAO staff study issued last March.

"In 1981," the GAO comments continued, "Sudan could not make scheduled payments of $365 million because export earnings were only $575 million. The U.S. offering of $75 million in new credits at high interest rates to a country as bankrupt as Sudan is unrealistic."