President Reagan responded today to what he called the "bad news" of 10.1 percent unemployment by pledging, at a carefully staged bill-signing ceremony, to find jobs for every American who is out of work.

The president warned at the ceremony that his opponents will try to make a "political football" out of the unemployment figures.

Reagan signed legislation intended to increase U.S. exports, and said that financial markets were casting "a solid vote of confidence in America's economy and her future."

" . . . The surge of investment in our bond and equity markets are telling us something very important," the president said. "America's economy is ready to lead the world out of recession and into recovery."

Reagan will continue his attempt to regain the political offensive on the economy Wednesday when, in another ceremony, he will sign a job training bill and give an address that the White House will ask the networks to televise.

Some White House aides hope the Wednesday ceremony, which will feature a group of job trainees, including a sizable number of minority-group members, also will help draw attention from the tribute scheduled that day for Secretary of Labor Raymond J. Donovan, a Cabinet member who has been something of an embarrassment to Reagan this year.

The backdrop for Reagan's vigorously delivered speech was a modern container vessel, the Sea-Land Explorer, which is capable of handling 859 containers weighing more than 20,000 tons. It was loaded today not with American goods for export but with containers of Japanese tape recorders, cameras and computer parts that had arrived from Yokohama the night before.

The president subsequently acknowledged to a television correspondent that he didn't have the slightest idea that the ship contained Japanese goods destined for American markets.

Reagan predicted, however, that the bill he signed today, the Export Trading Company Act of 1982, would create "several hundred thousand new jobs" by encouraging producers, freight companies and management firms to form joint ventures aimed at developing foreign markets. To allow U.S. products to compete more economically abroad, these joint ventures would be given antitrust protection.

The president called this bill, which had bipartisan support, "a high priority for our administration," and observed that attempts to pass similar legislation during the Carter administration had failed. Last Monday, during a question-and-answer session with employes of a high-tech company in Columbus, Ohio, Reagan seemed unfamiliar with the measure and quickly changed the subject when he was asked about it.

But today, Reagan was visibly confident as he accepted more responsibility for rising U.S. unemployment than he ever has before. After predicting that opponents of his policy would try to make "a political football out of the cruel fate" of the unemployed and repeating his familiar contention that past policies are responsible for the current recession, Reagan added:

"But to make it really fair, I'll tell you this. I guarantee you we're going to accept responsibility in this administration for finding jobs for all of the 10.1" percent of the work force without jobs.

His remark was greeted with a burst of applause by an audience of state and local officials, maritime union members and servicemen stationed here. Union leaders have been conspicuous by their absence during most ceremonies during the Reagan administration, but three maritime union leaders were on the platform with the president today when he signed the bill.

One of them, Jesse Calhoon, president of the Marine Engineers Beneficial Association, introduced Reagan and said he had done more than any other president since World War II to build up the Merchant Marine. Two Republican congressmen and Rep. Don Bonker (D-Wash.) also shared the platform with the president.

Reagan's promise today to find jobs for every American out of work appeared to conflict with his declaration of a week ago that an unemployment rate as high as 6.5 percent is now "normal" for the U.S. economy. The implication of that was that there is no ready way to reduce unemployment below that level.

But White House deputy press secretary Larry Speakes said Reagan meant what he promised today.

"He wants to put every American who wants a job back to work," Speakes said when he was asked whether the president had made a misstatement. "That's his goal."

The president went by helicopter to his mountain ranch northwest of Santa Barbara late today to spend the weekend. He is to make his weekly Saturday radio talk at 12:06 p.m. EDT, on the economy, and fly to Dallas for a political event Monday.