Banks have cut back sharply on lending to developing countries this year amid growing fears that poorer countries will be unable to keep up payments on their large debts, according to a report by Morgan Guaranty Trust Co.

This slowdown could seriously damage growth prospects in the developing world, the report says. Many international financiers now worry that if banks attempt to cut back too sharply on international lending, in the wake of payments problems in some countries, they may force otherwise relatively healthy nations into payments difficulties and economic retrenchment.

Last year U.S. banks boosted their net new lending to non-oil developing countries by almost one-fourth, Morgan Guaranty said. Other industrialized countries increased their lending by 20 percent.

In the first three months of this year, however, U.S. banks and their foreign branches reported an actual decline in outstanding loans to non-oil Third World countries. Overall, the industrialized nations showed virtually no net increase in lending to the developing countries in the first quarter of 1982.

The financial crisis that erupted in Mexico this summer fed bankers' anxieties about lending overseas and has made it very hard for any Latin American nation to raise new money, analysts say. One Chilean economist remarked recently that the Mexican crisis has hurt the economies of the whole region considerably by making banks wary of all debtors in Central and South America and unwilling to increase their loans there.

If banks stop making new loans to non-oil nations in the developing world, and merely maintained current loan levels, "real output growth in Latin America alone could be roughly 5 1/2 percent less" in the first year than if lending had continued to rise at last year's rapid rate, Morgan Guaranty estimates. Latin American nations are heavily dependent on bank finance to pay for their imports, and so would be particularly hard hit by a curtailment in bank lending from overseas. If banks lend debtor nations less money, then these countries are forced to buy less from overseas, and this in turn makes them grow more slowly because of a shortage of the imported goods used in the economy.

Such a sharp slowdown in lending -- equivalent to a cutback of about $50 billion in net capital flows -- is unlikely, analysts agree. From the point of view of the banks "a cessation of new lending to the developing coutries would be counterproductive," Morgan Guaranty says, as it would "be so large as to have a 'sledgehammer' effect on the major borrowing countries" and "jeopardize the ability of these countries to pay the interest on their existing loans."

However, banks are reducing their overseas lending to some extent, cutting the growth potential of many poorer countries. If banks increased net new lending to developing countries by 10 percent instead of last year's 20 percent, "in the first year the growth rate of the non-OPEC LDCs [less developed countries] would be about 1 1/2 percentage points lower than if a 20 percent rate of bank lending were maintained," Morgan Guaranty estimated. Latin American countries, under this scenario, could see a reduction in economic growth of as much as 3 percent "below that attainable if the faster pace of lending were continued," the study says.

The study points out that "in practice, it may be possible for some countries to sustain a sharp slowing in bank financing with a smaller impact on economic growth than indicated by these estimates, especially if imports can be reduced selectively through controls and a more realistic exchange rate policy." One of the major recommendations that the International Monetary Fund typically makes to borrowing countries with balance of payments problems is that they should devalue their currencies in order to encourage exports and discourage imports.