U.S. officials began a series of talks this week aimed at getting foreign suppliers to trim their shipments of steel to this country under President Reagan's program to reduce such imports through a series of voluntary agreements.

The president said his program should reduce steel imports to 18 1/2 percent from its present level of about 25 percent of the U.S market.

So far, talks have been held with three nations -- Argentina, Brazil and Spain -- singled out last month by U.S. Trade Representative William E. Brock for selling unfairly traded steel on the U.S. market.

The series of talks, which will continue with Japan and South Korea next week, were described as preliminary meetings at which no conclusions were reached. Trade sources in Brock's office suggested most negotiations require three to four sessions before an agreement is reached.

The talks are being held by Deputy U.S. Trade Representative Robert Lighthizer and the USTR's steel specialist, Charles Bloom. They met with Spanish officials in Madrid and Brazilian and Argentine representatives here. They meet with South Korean officials here today and will go to the Far East next week to meet with officials of Japan.

The greatest share of the import cuts will have to come from those five countries.

"It's just the first round with everyone," said Lighthizer. "It's a question of laying out where the cases are and where new cases will be." He added that in some instances he has indicated what the United States feels a country's import level should be.

The other major suppliers -- the European Community and Canada -- already are holding to their traditional share of the American market. There are talks under way with the EC, however, to set limits on its shipments of pipe and tube products to the United States.

The president, in his announcement Sept. 18, gave Brock 90 days to reach "surge control" agreements with countries that have sharply increased their sales in the United States. Among those countries are Spain, Brazil and Argentina.

All three will be under great pressure to cut their imports voluntarily, since penalty duties assessed as a result of findings that they are unfairly trading steel could increase the price of their products so much that they would be driven from the U.S. market.

Mexico and South Africa, two others countries accused of unfairly trading steel in the United States, agreed before the president's announcement to cut their shipments in return for having penalty duties dropped.

Brazil tried to do the same thing, but its offer was rejected because officials there did not go far enough.

Negotiations are considered especially difficult with Argentina and Brazil, however, since they argue that they need to export steel to earn the dollars to pay interest on loans to Western banks and multinational organizations.

The situation with Japan and Korea was described by Brock as a question of diversion that he said requires Tokyo to buy more Korean steel to take pressure off the American market. Imports amount to 4.9 percent of steel used in Japan, Brock said, forcing Korea -- the world's most efficient steel producer -- to ship steel across the Pacific Ocean to the United States instead of selling it to nearby Japan.

There are reports in steel trade circles that Japan has indicated a willingness to talk to Korea about buying more steel. The job for the U.S. negotiators, sources said, is to get assurances that Korea will sell Japan steel earmarked for America instead of using the new market opening to increase its total exports.

Korea also has a closed market, trade sources said, and has a small number of unfair trading cases pending against it.

Congress, in the closing days of the session, gave the administration the authority it needs to enforce voluntary restraint agreements by allowing the U.S. Customs Service to issue "visas" for imports. These "visas" would be limited by the amount of steel a country said it would ship to the United States.

There are fears, however, that these voluntary quotas could be circumvented as easily as quotas on textiles -- by transhipping steel through another country that either has no quota or has not met it.