The White House announced yesterday that seven countries have agreed to cut steel exports to the United States by about 30 percent as a result of President Reagan's program to reduce the penetration of foreign steel into the American market.

The restraint agreements fell short by 1 or 2 percentage points of the president's goal of cutting total imports to 18 1/2 percent of the U.S. market from their present level of about 26 percent, administration officials acknowledged. They also conceded the cutbacks are likely to increase the cost of steel to the American consumer.

"The president is very pleased with the successful completion of these negotiations," said White House spokesman Larry Speakes. "He considers these agreements to be a step in the right direction," giving the American steel industry time to modernize so it "will be able to compete in the world market."

The president was so pleased, in fact, that he transformed the planned, routine announcement by the U.S. Trade Representative's Office into a full-scale White House briefing.

The industry's response was moderate. Donald H. Trautlein, head of the American Iron and Steel Institute and chairman of Bethlehem Steel Corp., said that "considerable progress has been made," but called for "forceful action" by the government to increase the number of exporting nations willing to cut their U.S. sales.

U.S. Steel Corp. Chairman David Roderick said he was "satisfied" with the restraint agreements, but his company filed 28 unfair trade complaints yesterday accusing eight countries of subsidizing steel for export or dumping it on the American market at less than its value.

Fred Lamesch, president of the American Institute for Imported Steel, attacked the agreements, which he said "will prove chaotic and injurious to the American economy, American steel users and manufacturers who export."

Deputy U.S. Trade Representative Robert Lighthizer said the United States now has restraint agreements with countries that supply 75 percent of imported steel to the United States. These include the seven nations whose agreements were announced yesterday -- Japan, South Korea, Brazil, Mexico, Spain, Australia and South Africa -- as well as the European Community, which agreed two years ago to cut exports to the United States.

Lighthizer will go to Canada today. He is expected to tell the government there that the Reagan administration left Canadian steel makers out of the negotiations in the expectation that they would not try to increase their penetration of the American market above its present 3 percent level.

The latest restraint agreement will cut the penetration of steel imports from just the seven nations to 10.1 percent from 14.4 percent of the American market, Lighthizer said.

"We accomplished everything we set out to accomplish in 90 days" since the president announced his program to cut imports, he added. "But that is just the beginning. It is a five-year program, and it will take five years of work."

The president proposed the import restraint agreements as an alternative to a recommendation of the International Trade Commission to reduce foreign steel sales through quotas and higher tariffs.

Argentina, which supplies 0.3 percent of foreign steel in the United States, has refused to cut its imports, and Lighthizer said he is "not optimistic" about reaching an agreement. Unfair trade cases might have the same effect, steel analysts said.

The downside of the president's program is higher prices, which the Congressional Budget Office estimated could total $3.4 billion over the next five years. Steel executives, however, said the industry needs the extra income to pay for an intensive modernization program.