Treasury Undersecretary Beryl Sprinkel yesterday challenged a contention that the International Monetary Fund's short-term resources would be exhausted by another loan approximating the $5 billion package now being considered by the IMF to ease Mexico's financial crisis.

This assessment had been made by economist John Williamson of the Institute for International Economics. The institute released a report Tuesday urging a large boost in the IMF's lending authority.

"That's wrong," Sprinkel said in a telephone interview. "It's not even in the ballpark." He also said that the private group's recommendation for a boost from $67 billion to $110 billion in IMF quotas -- national currencies deposited by member countries -- was "too much," and that nothing approaching that figure would be supported by the United States.

The subject of IMF quotas will be a leading item on the agenda for the annual meeting of the IMF in Toronto Sept. 6-9.

Sprinkel said that the IMF presently has about $26.5 billion in undisbursed and uncommitted funds, made up of about $16.5 billion in ordinary resources, and around $10 billion in unused borrowing lines from major central banks, through the General Agreements to Borrow, or GAB. After lending Mexico about $5 billion, the IMF would still have more than $21 billion left, Sprinkel said.

He conceded that "this doesn't mean that, under all the circumstances you could imagine, the IMF could handle all possible problems." But he said his tally clearly showed that the IMF's funds would not be exhausted even by a duplication of the Mexican drain.

Williamson had said the Mexican situation demonstrated that "the fund's short-term liquidity position is even tighter than we thought." In response to data cited by Sprinkel in his rebuttal, Williamson said in a conversation yesterday that perhaps the IMF's funds technically would not be exhausted by another large borrowing equivalent to Mexico's, but that "it would leave the IMF in a position where it would be difficult to finance another large one after that."

He said, first of all, that the GAB funds should not be counted among the IMF's short-term resources, because such funds are available for lending only to GAB members, the wealthiest nations in the world. IMF sources confirmed that use of GAB funds is restricted in this way.

As to the IMF's ordinary and uncommitted resources, which Sprinkel put at $16.5 billion, Williamson said that his group's calculation shows only $10 billion.

He suggested that part of the discrepancy "lies in the fact that there's a certain ambiguity in how much of these currencies is really usable for lending. It could be that the figure is $12 billion or $13 billion, but I think his Sprinkel's figure is still on the high side."

He noted, nonetheless, that "both Sprinkel and I forgot that there's 4.6 billion of special drawing rights in the IMF general account." SDRs, the international currency issued by the IMF, are worth about $1.09 each. The SDR pool would add about the equivalent of $5 billion to the IMF's lendable resources. But Sprinkel said he had included the SDRs in his estimate of $16.5 billion.

As to IMF quota increases, Sprinkel said the Reagan administration could not justify the appropriations increases that would be required for American participation in a vastly enlarged fund. "Besides", he said, "we don't think it's needed."