A group of Republican legislators from steel-making states went to the White House yesterday in a last-ditch effort to persuade President Reagan to impose quotas and higher tariffs on steel imports.

The president has until Sept. 22 to rule on an International Trade Commission recommendation that would subject 70 percent of all steel imports to quotas and higher tariffs for the next five years.

But Reagan has resisted most efforts to restrict what he sees as a free trade among nations, and only last week he rejected a similar petition for import protection filed by U.S. copper producers. The president overruled the ITC and turned down advice from Interior Secretary William P. Clark in denying the copper companies' request.

But the Republican law makers -- 13 House members and eight senators -- expressed optimism for their cause after a 45-minute meeting yesterday afternoon with the president and David A. Stockman, director of the Office of Management and Budget.

"We think that the president understands the sensitivity of the issue," said Sen. John Heinz (R-Pa.), whose state has been among those hardest hit by plant closings and layoffs in the domestic steel industry.

Heinz led the senatorial delegation. He said that both senators and House members emphasized three points during the meeting:

*The steel issue is different from the copper issue. Domestic steel makers have proved in more than 150 cases before the ITC that foreign competitors have been dumping their government-subsidized products in the U.S. market, while restricting U.S. and other steel exports to foreign markets.

*Any action by the Reagan administration restricting steel imports has to be comprehensive. Foreign steel makers can get around partial restrictions simply by increasing their production and shipment of steel products such as pipe and tube that are not affected by restraints.

*Reagan's current popularity, even in steel-making states, in the presidential race against Democratic hopeful Walter Mondale will nosedive if there is no strong administration action on steel.

Rep. Don Ritter (R-Pa.), whose northeastern Pennsylvania jurisdicition includes the economically hard-bitten city of Allentown said, "Most of our people feel that the president is not going to let them down, which is why he is still popular with many of them," he said. "But if he does let them down, those feelings could change overnight."