Propelled by fears that the Third World's debt crisis could trigger a depression, the International Monetary Fund will act this week to expand--probably by about 50 percent--the resources available to it for loans to both industrial and developing nations.

As a result of that action, and one taken separately by the United States and other rich nations on Jan. 18 to expand an emergency fund for similar purposes, the Reagan administration soon will ask Congress to authorize almost $10 billion for these new commitments.

Although the $10 billion would be a financial transfer and not a budget outlay, indications are that the administration will have a rough time in selling it to Congress. "I think we had better fasten our safety belts," Sen. Charles McC. Mathias Jr. (R-Md.) said in a telephone interview yesterday.

Mathias said that "the first reaction I get from members of Congress is: 'Why should I vote $10 billion to bail out Citicorp or the Chase Manhattan Bank?' "

Congressional resistance to strengthening the international lending agencies has a long history, but is accentuated now by the deep recession. The Reagan administration compounded the problem by initially opposing any major boost in the IMF's lending power, before dramatically reversing its position last fall.

Mathias said yesterday "it will now take the concerted resources" of the administration and IMF supporters like himself to persuade Congress that raising the IMF loan funds will prevent defaults on loans by U.S. banks, and thus ultimately protect jobs and improve the domestic economy.

The IMF policy board, the Interim Committee, will meet Thursday and Friday and is poised to boost member nations' quotas, or deposits, by almost 50 percent. A full 50 percent boost would raise the IMF's theoretical capitalization from 61 billion special drawing rights (SDRs), or $66 billion, to 91.5 billion SDRs--the equivalent of $99 billion.

The Interim Committee meetings, led by British Chancellor of the Exchequer Sir Geoffrey Howe, will be preceded by a session of the Group of Twenty-Four nations, representing the Third World countries, who are expected to ask the richer ones to do even more.

Reflecting anticipated congressional resistance, Treasury Secretary Regan has been careful to say that he has agreed only to an increase of "between 40 and 50 percent."

But some American sources said yesterday they expected that either the United States would go all the way to the 50 percent figure or, at worst, will agree to a "rounded-down" 90 billion SDRs, or $97 billion, the equivalent of a 47 percent increase in quotas.

A 50 percent quota increase combined with the Jan. 18 boost in the emergency fund known as the General Agreements to Borrow (GAB) will add nearly $30 billion to the IMF's stock of "lendable" funds, which will have dwindled to $8 billion at the end of this month, according to sources.

Only a part of the IMF capital that comes from member quotas actually is usable for loans to others. Thus, of the anticipated $30 to $33 billion quota increase, only about half, or some $16 billion, will be in hard currencies or SDRs.

An additional source of hard currency will come from the Jan. 18 GAB agreement, when the rich nations boosted their stand-by credits from $7.1 to $19 billion, and also made this available to all IMF nations, not just the rich nations themselves. The United States accepted a 25 percent share, or $4.25 billion, about half of which will require a new authorization from Congress.

When the $12 billion increase from the expanded GAB fund is added to lendable funds from increased quotas, the loan agency would have about $28 billion added to its lendable resources.

This is not an enormous sum measured against the $500 billion to $600 billion in overhanging Third World debt, according to supporters of generous quota increases.

As recently as the annual meeting of the IMF in Toronto last September, the administration advocated limiting the quota increase to no more than 25 percent. Although Regan says that was "a bargaining position," others say that a dramatic shift in the American position came only after it became apparent that a big rollover of Mexico's external debt was unavoidable.

That touched off a curtailment of commercial bank credit to all of Latin America, and was followed by a liquidity crisis in Brazil.

The increased U.S. commitment to the GAB, plus its share of the larger IMF quota, accounts for roughly the $10 billion mentioned by Mathias. But because the United States would get offsetting credits in the form of financial reserves on the IMF books, there would be no net budgetary impact.

The major powers already have agreed informally that, because of the urgency of the international debt crisis, an effort will be made to make the new quotas effective by the end of 1983, or two years earlier than would have been the case normally. This was a suggestion initiated by the U.S. government.

Still to be settled is allocation of the additional $30 billion to $33 billion of quotas--which determine voting shares in the IMF.

Presently, the United States has a 19 1/2 percent share, well over the 15 percent which effectively allows it a veto. American officials said yesterday that the administration is willing to go along with a reallocation that brings quotas "more in line" with the relative importance of nations to the world economy, slightly reducing the relative U.S. share.