America's allies would like the Reagan administration to put up or shut up on its oft-stated commitment to rely heavily on the multilateral institutions like the World Bank and the International Monetary Fund to help solve economic problems of developing countries.

In today's pressure-packed world, which daily sees headlines for such developments as the nationalization of Mexico's banks, and the threat of defaults elsewhere in Eastern Europe and Latin America, the only way in which the bank and the IMF can play a lead role is if they both have enlarged resources, most of the other nations say.

This has been the message hammered home time and again by World Bank President A. W. Clausen -- a California Republican who pulls no punches in demanding better support from the United States -- and by IMF Managing Director Jacques de Larosiere.

De Larosiere feels it is essential that the IMF quotas -- currency deposits made by members -- be increased from the present rough equivalent of $67 billion to a minimum of $110 billion, and possibly to $125 billion. This, then, would be the pool of money available for lending to developing nations, beginning about the middle of the decade.

But as the annual IMF-World Bank meeting gets under way here, with anxiety spreading about the viability of the international banking system, and deepening gloom about prospects for any significant global economic recovery, the Reagan administration insists that any expansion of IMF resources should be held to a minimum. Moreover, the Washington authorities have actually cut their contributions to the World Bank's subsidized aid program.

Whenever President Reagan goes to a summit meeting -- as he did last October in Cancun, and again in June at Versailles -- he endorses in principle American reliance on the fund and bank as preferable to more radical aid programs floated through the United Nations. This American "commitment" was restated as recently as Wednesday in Washington by Treasury Secretary Donald T. Regan. And Regan -- who is also U.S. governor for the bank and fund -- will use similar words in his address to the plenary session here on Tuesday morning.

But, the Europeans and the poor nations ask, what lies behind the words? Once within the convention halls of the IMF-bank meeting, the U.S. contingent puts aside its summit-level assurances, and engages in what has to be described as a foot-dragging exercise. Almost alone, they minimize the need for a large increase in IMF or World Bank resources, in part because of the assumed difficulty in getting appropriations through Congress.

Treasury Undersecretary Beryl Sprinkel says a doubled IMF quota would cost the United States $14 billion in appropriations. But former Treasury assistant secretary C. Fred Bergsten points out that the U.S. quota in the fund does not show up as a budget expenditure or run up the deficit. Congress traditionally, Bergsten says, has been more receptive to IMF funding than it has to putting up money for other international agencies.

Nonetheless, the Treasury has been working on some sort of emergency fund, outside of IMF quotas, that could be used in a global emergency. But Regan himself has admitted that any funds that the United States provides in this manner would also have to be approved by Congress.

"I think this is a pretty critical meeting," Bergsten, now head of a new Washington think-tank, the Institute for International Economics, said in an interview with The Washington Post.

"It would be very unfortunate if decisive action were not taken. The Mexican problem highlights the possibility of a large number of countries having to come into the IMF for substantial amounts of money. And the IMF participation in programs of that type is absolutely essential to encourage other lenders .

"For the fund to deal with the problem, there are two steps needed. One, is to at least reach substantial agreement on at least a doubling of quotas for the longer-run period. And second, to deal with imminent problems, to reach agreement on an interim facility that will substantially augment IMF resources between now and 1985."

To tide things over -- patching up the leaks in the system from such disasters as the Mexican crisis -- the IMF will need to borrow several billion dollars. After coming up with nearly $5 billion as the linchpin of the Mexican bail-out, the IMF feels, its lines of credit will be exhausted, and its normal funds at a precariously low point. Bergsten would prefer something like the lending "facility" named after former IMF head Johannes Witteveen, in which the major nations would make available to the IMF up to $20 billion to use until enlarged quotas go into effect in 1985.

"For 20 years," Bergsten said, "IMF quotas have always been too small. Look back at the record of what actually happened: in the 1960s, the General Agreements to Borrow had to be created. After the first oil shock, the 'oil facility' had to be created to augment their resources. Then, there was the Witteveen facility in 1978. In the last couple of years, the IMF had to go to Saudi Arabia for a big loan. So for 20 years, the record shows that the IMF's quotas turned out -- after the fact -- to be too small for what the members of the IMF wanted the institution to do."

The general thrust of this argument was echoed by John Petty, head of the Marine Midland Bank; and Jim Greene, president of American Express International Banking Corp., speaking for a blue-ribbon group of prominent business and labor leaders and economists who said it is in the self-interest of the United States to continue strong support for both the fund and the bank.

Their panel, under the aegis of the United Nations Association of the U.S.A., said in a report that the IMF will become ineffective without "at least a doubling of the current level of the fund's quotas."

The Petty-Greene group also urged the United States to "honor fully and promptly" its commitment of $3.2 billion for the International Development Association -- the bank's soft-loan agency -- in a three-year period ending fiscal 1983. But the United States has already stretched its commitment to four years. And since other nations drop their shares, pro rata, IDA in the past year suffered a shortfall in available funds from $4.2 to $2.8 billion.

That, of course, places the next replenishment of IDA funds -- the 7th, due in 1984 -- in jeopardy. It already is apparent that IDA-7 will be delayed in its starting time by a year, and IDA will have to scrounge for funds, in a patchwork way.

Clausen told this reporter that there must be a continuation of IDA, but he also concedes that IDA-7 will have a different "shape," meaning that the days of zero-interest for IDA borrowers are probably coming to an end.

But beyond the immediate and specific problems of IDA, there is a conceptual gap between the way the present American Treasury views the World Bank and the other multilateral development banks (MDBs), and the way most of the other nations here see the issue.

The current administration views things through private-sector tinted glasses: it sees its participation in the MDBs as primarily linked to American global or political objectives, rather than the economic development of the Third World.

Although a year-long Treasury report cleared the World Bank of the charge that it is "socialist," the Reagan administration still has an arms-length approach to the bank in which it presses for more reliance on the private sector, and faster "graduation" of nations up through what it regards as the coddling process of IDA and the bank, and out into the commercial world.

The Petty-Greene report observes that "the proposed cutbacks in U.S. contributions to the MDBs are not justified in light of the needs of the developing world for external financial assistance and in light of the unique ability of the World Bank and the regional development banks to help in meeting those demands."