In a move to aid the ailing steel industry, the Reagan administration said yesterday that it will ask the European Economic Community next week to agree to "voluntarily" restrain steel shipments to the United States.

President Reagan said during a half-hour meeting with the heads of the nation's top three steel companies that he will direct Commerce Secretary Malcolm Baldrige to discuss the possiblity of "working out an accommodation on steel imports," according to White House spokesman Larry Speakes.

White House sources said the accommodation will be much like the "voluntary" agreement the administration worked out with Japan last spring after American automakers said Japanese cars were taking an increasingly large share of the American market and aggravating their depressed condition.

Baldrige will tell the Europeans in meetings in Brussels next Wednesday and Thursday that continuing to send cheap steel imports here would not be in their best interests and that the administration is receiving strong political pressure to do something about the problem, a White House source said.

The steelmakers "expressed a willingness" to postpone filing complaints of unfair trading practices against the Europeans until Baldrige returns with a report, Speakes said.

U.S. Steel Corp. Chairman David M. Roderick had threatened to file at least nine complaints against European and other steelmakers who he said were dumping steel here, that is, selling it below what it cost them to make it and injuring American steelmakers in the process.

In an effort to forestall the steel industry from filing complaints, last month the Commerce Department filed its own against Belgium, France, Brazil, South Africa and Romania. But Roderick said the Commerce Department's efforts would not be enough and that he would file cases of his own. On Monday Roderick said he would postpone filing any complaints until he met with President Reagan.

The Commerce Department's complaints will "continue to be pursued for the time being," a White House spokesman said.

Present at the meeting yesterday were Roderick; William DeLancey, chairman of Republic Steel Corp.; Donald Trautlein, chairman of Bethlehem Steel Corp.; and Robert Peabody, president of The American Iron and Steel Institute. None of them were available to reporters immediately following their meeting.

Last spring when President Reagan urged the Japanese to "voluntarily" restrict vehicle exports to the United States, he was criticized by proponents of free trade, who said the action contradicted the president's espoused philosophy.

But Speakes said yesterday that the accommodation "is generally the administration's philosophy, a free-trade philosophy. That would be in line with the president's philosophy."

The steel issue threatened to increase tension between the United States and Europe at a time when the Europeans already are blaming the administration's economic policies for their depressed economies. The EEC said when the Commerce Department filed its own cases that the administration was taking a "dangerous course."

There was no immediate comment yesterday from the EEC.