President Reagan reaffirmed his commitment to free trade yesterday, but promised under intense protectionist pressures from Congress to act against trading partners who close their markets to U.S. products.

As a signal of his seriousness about cutting America's massive trade deficit, Reagan announced during his regular weekly radio broadcast that he has ordered investigations into unfair trade practices by three countries -- Brazil, Japan and South Korea -- and set a Dec. 1 deadline for the resolution of two other cases in which Japan and the European Community were found to have violated international trade laws.

"We hope that . . . we will be able to convince our trading partners to stop their unfair trade practices and open those markets that are now closed to American goods. We will take countermeasures only as a last resort," the president said.

"Our trading partners should not doubt our determination to see international trade conducted fairly with the same rules applicable to all," Reagan added.

By calling for investigations, which could take as long as a year to complete, and pressing to settle old cases, Reagan stopped far short of congressional demands that he set tariffs and quotas to protect American industries.

But the president stuck to his free-trade philosophy in the face of the worst trade deficit in the nation's history, insisting that "protectionism costs consumers billions of dollars, damages the overall economy and destroys jobs."

Reaction was swift from Democrats, who are trying to develop trade as an issue they can use in next year's congressional elections. Making his party's response to the president's radio address, Rep. John P. Murtha (D-Pa.) called for stronger presidential action.

"Citizens can't understand why we refuse to get tough with our trading partners," he said. "They admire America for standing up to the communists with a strong defense, but they can't understand why the Reagan administration refuses to be equally tough on world trade."

While approving the president's approach, Sen. John C. Danforth (R-Mo.) questioned whether it signaled "a new policy of the enforcement of American rights in international trade agreements or is a grudging bone tossed to Congress" in an attempt to stop passage of some 300 protectionist trade bills in the hopper this year.

U.S. Trade Representative Clayton Yeutter, charged by Reagan with carrying out the investigations, said the president's moves were designed to "provide motivation" to trading partners to open their markets. The import of the step, he said, was that it is the first time a president has used his legal authority to initiate unfair trade cases.

Specifically, the president called for investigations against what he called "three cases of unfair trade" -- a Korean law that bans U.S. life and fire insurance companies from selling in that lucrative market; a Brazilian law that limits foreign computer sales, and Japanese restrictions that lower sales of U.S. tobacco products.

In addition, he called for quick action to resolve two cases in which General Agreement on Tariffs and Trade panels have found practices that violate international trade agreements. They involve Japanese restrictions on sales of leather and shoes and European Community subsidies of canned fruit.

None of the cases are new -- Yeutter said he was negotiating increased sales of U.S. tobacco in Japan 12 years ago when he was an assistant secretary of agriculture -- and they involve a total market of $15 billion. They were chosen, however, for their specific messages to trading partners. The case of the canned fruit subsidies, for example, was seen as a way of telling the European Community the United States will not stand for delays in GATT dispute settlement.