Among the skirmishes in Washington's current budget-cutting battles is one that could have permanent effects on the United States' 42-year, love-hate relationship with the United Nations. At issue is whether President Reagan can persuade Congress to pay enough of the nation's $414 million in back dues to avoid the risk of the Soviet Union supplanting U.S. influence in the world body.

Two recent events underlined the dilemma confronting Reagan. One was in the form of a letter to Reagan from U.N. Secretary General Javier Perez de Cuellar warning that the United Nations is on the brink of bankruptcy and will be unable to cover its expenses in December unless the United States pays a substantial part of this year's dues by that time.

Perez de Cuellar's letter came shortly after the Soviet Union, in a major change of policy, announced that it will pay all of its U.N. debts and will work to strengthen the U.N.'s role as a neutral force in resolving international disputes.

The reasons for the Soviet move are not clear. Some Western diplomats believe it reflects an attempt to shift some of Moscow's costly Third World entanglements into the United Nations at a time when Soviet leader Mikhail Gorbachev wants to focus on radical economic changes at home.

Among U.S. officials, though, there is strong suspicion about Gorbachev's proposals to expand the United Nations' role in such areas as arms-control verification, human-rights enforcement, antiterrorism activities, controlling outer space and the environment, and resolving regional conflicts such as the Persian Gulf war. In the U.S. view, the Soviets aim to change the United Nations in ways that would favor the Kremlin's political agenda at the expense of the West.

The Soviet's U.N. move comes as the United States, which for years could demand a considerable say in U.N. affairs because it put up 25 percent of the annual budget, faces possible suspension of its vote for nonpayment of dues. The circumstances seem likely to strengthen Soviet influence among Third World countries, the majority of the 159 member states.

"We risk turning the leadership over to the Soviets," Deputy Secretary of State John C. Whitehead said in a recent interview. "In our view, that is a most unfortunate development for which we will pay dearly in the future."

Said a U.S. official: "America's status in the United Nations is starting to look like that of the aging millionaire who asked his mistress whether she'd still love him if he lost his money, and was told: 'Of course, I'll love you, daddy. And I'll miss you too.' "

But many members of Congress and Reagan's hard-line conservative supporters say the problem is that the United Nations often repaid its American sugar daddy by being unfaithful. Over the years, simmering resentments over perceived anti-Americanism periodically have erupted in demands for the United States to quit the United Nations or to limit how much taxpayers' money gets spent there.

With austerity now the watchword on Capitol Hill and Congress cutting the U.S. foreign policy budget, many members of Congress say the temptation to take sizable bites out of U.S. contributions to the United Nations has been bolstered by a sense, built up during almost seven years of the Reagan presidency, that the administration does not consider the organization to be of great importance to its foreign policy goals.

As proof that the administration seems aligned with those who believe U.N. membership is a waste of money, they point to continuing rhetorical clashes between U.S. delegates and critics from Third World and communist countries; administration allegations that the Soviet Union's U.N. diplomats spy on the United States; and running battles with other members about the need to curb spending and bureaucratic growth at the international body.

While acknowledging that it often is among the United Nations' severest critics, the administration insist this does not mean it thinks the United States should be on the outside.

Said Whitehead: "We support the United Nations. We are in favor of it. We were the leading country in founding it. But we'd like to see it work to our interest, which it hasn't always done. We have been particularly concerned about its administration and budgeting process, and we believe strongly that these should be reformed because the staffs are too large and the budgets runaway. The administration has tried for 6 1/2 years to follow a track of support on the one hand and on the other pressing for reforms and changes to improve its administration and reduce its budget."

Other U.S. officials said his statement reflects the administration's view that the United Nations, for all its flaws, remains a convenient forum for dealing with international problems that cannot be handled in other ways. They cite as evidence U.S. efforts in the Security Council to fashion a sanctions resolution to put the world community behind an arms embargo against Iran as a way of exerting diplomatic leverage in the Iran-Iraq war.

Despite this, the administration has not relaxed its campaign for major internal U.N. reform. The move has sharpened differences with Third World members, particularly those from Africa, who have become accustomed over the years to regarding the United Nations as an international pork barrel where they can use their majority voting status to obtain a disproportionate share of jobs and program funding.

A year ago, the administration, spurred by growing congressional irritation at the situation, joined the Soviets and other major contributors to negotiate an agreement with the Third World bloc that budget ceilings and spending priorities would be decided by consensus rather than majority vote. This would give the few big donors greater influence. But, in return, the United States and other debtors were supposed to clear up their arrears.

The $414 million U.S. dues debt includes the entire $212 million that the United States was assessed for the 1987 regular budget. Congress has not yet decided on a final figure for fiscal 1988 contributions, although the Senate tentatively would provide $141.7 million and the House $97.5 million, before the deductions required by the Gramm-Rudman-Hollings budget law are made.

A final figure in that range would prevent the United States from increasing its contribution over the $100 million it paid last year. A payment that small would put Washington in the position of reneging on its commitments under the reform agreement. Opponents of reform have stalled implementation of the agreement, and U.N. officials say that the opposition has been fueled greatly by arguments that the United States doesn't intend to honor the bargain.

By contrast, the Soviet Union, long the major debtor with unpaid obligations stretching back to the 1950s, has paid its current dues of $100 million and has indicated that it intends to pay arrears of about $200 million, most of it resulting from past U.N. peacekeeping operations that the Soviets opposed.

These additional Soviet payments won't be made in time to cover the shortfall that in December is expected to prevent the United Nations from paying the monthly salaries of up to 12,000 employes.

If that happens, a U.S. official said, "there will be havoc throughout the organization, and the blame will be placed on the U.S. dues deficit. The resulting resentment among the other members almost certainly will deny us the fruits of the victory we won in the reform agreement. It also will create an intense resentment of the United States on which the Soviets can capitalize by putting up a few more dollars that will permit them to pose as the new saviors of the U.N. It will be a real steal and bargain for them."