American business and labor leaders asked President Reagan yesterday to take a tough stand on economic issues in today's much awaited meeting with Japan's new prime minister, Yasuhiro Nakasone.

The pleas of the Americans, who cited the distressed U.S. economy and Japanese trade practices, blended with the sound of sirens from the arrival motorcade as the Japanese visitor and his party sped past the White House into town for a three-day official visit.

According to business participants in yesterday's meeting, Reagan listened carefully, but did not disclose the plans for his presentation to Nakasone. However, a senior adminstration official forecast that Reagan will walk "a very delicate line" between praising Nakasone for unusually vigorous efforts during his seven weeks in office and requesting additional "prompt action" to meet U.S. concerns in both economic and military fields.

There was no indication that Reagan will shift his basic stand, which was worked out in a meeting with his senior advisers Friday morning. As explained by administration sources, Reagan's central objectives will be to establish a close working relationship with the new Japanese leader and to convince Nakasone that rising protectionist sentiment in this country is a formidable political problem with major dangers for both partners in the Tokyo-Washington alliance.

There is no expectation in the administration, according to the sources, that Nakasone will be able to pledge substantial additional actions during this week's meetings. The hope is, though, that he will use the discussions to set the stage for further action after returning to Tokyo.

"I think it is a little unwise to expect a whole range of specific measures to come out of a first meeting between the president and the prime minister," said U.S. Trade Representative William E. Brock, a key participant in economic negotiations with Japan. "The important thing is to recognize the need for continuing action over a period of time. Nakasone has taken some steps already. Further steps will be needed."

One topic at yesterday's White House meeting, according to Ford Motor Co. Chairman Philip Caldwell and United Auto Workers President Douglas Fraser, was their request that Japan extend its "voluntary" limit on automobile exports to the United States.

A Kyodo news agency report from Tokyo quoted Ministry of International Trade and Industry officials as saying that Japan will agree to continue the two-year-old limit for a third year beginning April 1, at the existing ceiling of 1,680,000 automobiles per year.

Fraser said outside the White House, however, that his union and the automobile industry want the import limitation to be "scaled down" in number and to be extended for two years, rather than one, because of the slump in U.S. auto sales.

According to Caldwell, the "central issue" behind the soaring U.S. trade deficit with Japan is the misvalued ratio between the dollar and the yen. The recent 20 percent increase in the value of the yen, an unusually sharp change, goes "about 40 percent of the way" and is "good progress" toward a proper ratio, the automobile executive said.

Among the other trade issues to be discussed, according to a White House briefing for reporters, are pending U.S. requests for "a substantial liberalization" of Japanese import quotas on beef and citrus fruit. Those requests have met strong resistance from agricultural interests in Japan.

"The overall mood in the United States is to get tough with Japan" on this and other issues, said Robert B. Delano, president of the American Farm Bureau Federation, as he left the White House meeting yesterday. Delano said his impression is that "the president will be tough . . . . He's listening."

On the military issue, Nakasone will be asked to take tangible new steps toward being able to defend Japan's home islands and protect sea lanes up to 1,000 miles away. In the U.S. view, these aims were accepted by Nakasone's predecessor, Zenko Suzuki, in his Washington visit in May, 1981, but Japanese forces are far from adequate to fulfill them.

Assistant Secretary of Defense Francis J. West said recently that it would be the 21st century before Japan could perform these missions, at the present pace of its military efforts. A joint Japan-U.S. study group, composed primarily of military officers, is to begin meeting in Tokyo within a few weeks to define further the requirements of the home defense and sea lanes missions.