The debt-battered economies of Latin America were overwhelmed by financial problems last year that appear to have turned even worse in the early months of 1988, the Inter-American Development Bank said Saturday.

In its annual assessment of social and economic conditions in the region, the bank said the crisis was hitting poorest people the hardest as countries made further cuts in spending on social programs.In a briefing for reporters, bank president Enrique Iglesias said "the situation in Latin America continues to deteriorate with 1987 being worse than 1986 and our preliminary estimates indicating that probably this year will be substantially worse than last year."

Bank officials said that figures for the first half of this year indicate that five countries in Latin America - Argentina, Brazil, Mexico, Venezuela and Peru - will suffer economic downturns this year although there could be some improvement during the current six months.

The report said that the rate of economic growth dropped from the 3.6 percent average achieved in 1984 through 1986 to only 2.6 percent in 1987.

It said that in 1987 three of the region's four largest economies - Argentina, Mexico and Venezuela - grew less than two percent, and Brazil's rate was just under three percent.

Only Colombia, Chile and Uruguay had growth rates of 4.9 percent or more in 1986 and 1987.

Led by Brazil and Mexico, the region last year had a gross domestic product of $900 billion. The report said the dominance of these two countries was, if anything, increasing.

The report said the size of the economy on a per capita basis, the key measure of economic well-being, was lower in 1987 than in 1980 in most countries of the region.

"The deterioration of Gross Domestic Product per capita comes at a time when fiscal spending is being cut back and alternative employment programs and safety nets are inadequate. It is therefore likely that the data understate the worsening situation of the lower income population," the report said.

The bank said that while the region is struggling with economic crisis and social dislocations, it has implemented sweeping economic reforms.

Seeking new ways to earn foreign exchange to allow it to pay its debts and import badly needed goods, the region has increased the amount and the kind of products it exports.

In part, this reflected Mexico's experience in the early 1980s, when its economy was rocked by a slump in the price of oil, its main source of export earnings.

Since then, with the developing banks looking on, the region has attempted to diversify exports, looking for a variety of ways of earning foreign exchange.

The report said that Latin America increased its volume of exports by 4.4 percent annually in the 1980s, compared with a 2.6 percent growth rate in world trade.

In 1987, Latin America's volume of exports reached an unprecedented high, moving up 35 percent over 1980.

Governments in the region also continued belt-tightening efforts, notably by cutting their budget deficits. In some countries - Bolivia, El Salvador, Guatemala, Honduras, Uruguary - the cuts have been dramatic, the report said.

Despite efforts at reform, funds continued to flow out of the region as countries repaid their loans but were not able to get much new money to finance development.