Japanese Prime Minister Yasuhiro Nakasone told President Reagan yesterday that he will aim to build Japan's air defense to the point that it can detect and stop overflights by the Soviet Union's long-range Backfire bomber.

Acceptance of such a mission would require a major buildup by Japanese forces beyond what is scheduled.

In an interview with Washington Post editors and reporters, the outspoken Japanese leader also said it will be a "quite clear" aim of his administration to be able to bottle up the submarine and surface ships of the Soviet Pacific fleet in the Sea of Japan through the control of several strategic straits.

U.S. military leaders long have sought Japanese agreement to undertake these missions, which are of major strategic importance even though they could flow logically from Japan's strictly defensive military posture. But until now, Japanese prime ministers have not endorsed such missions publicly.

Nakasone's boldness in the military area, as well as unusually direct and forceful statements in the economic field, were greeted appreciatively by Reagan and other senior administration officials.

The conviction of top U.S. officials that the new Japanese leader is a man they can work with is reportedly one of the factors behind Reagan's decision to continue the talks with Nakasone in a previously unscheduled breakfast meeting today.

On the economic side, Reagan and Nakasone pledged to work together to resist protectionism and revitalize the global economy. But they forged no new solutions to the vexing trade problems between the capitalist world's two most powerful industrial countries.

Before the White House meeting, Nakasone told Post editors that the time has come to place political limits on Japanese economic expansion abroad, lest the island nation become isolated from its trading partners and the world at large.

He compared the dangers of unrestrained Japanese economic expansion today with the unrestrained Japanese militarism that led his country into World War II. A central task of Japanese political leaders, according to Nakasone, must be to prevent the isolation of Japan by accommodating its economic drives to the needs of other nations.

Today's breakfast is to be attended by the two leaders, Nancy Reagan, Tsutako Nakasone and the Nakasones' younger daughter, Mieko, a former announcer for NHK, Japan's national public broadcasting system.

Administration spokesmen said that, despite the presence of family members, the discussion will be substantive and is expected to center on East-West relations, arms control and other international problems.

Reagan may use the breakfast session to emphasize again, as he reportedly did in yesterday's 2 1/4-hour meeting, that the protectionist drive in the United States is a serious political problem for both nations and a hazard to the world economy.

According to a Japanese briefing, Reagan also made a domestic political point, telling Nakasone that Democrats had used "unfair" trading by Japan as a slogan in recent months and predicting that "if the Democrats win in 1984, protectionism will triumph."

The two leaders did not discuss one of the most difficult trade issues between their countries, the continuation of Japan's two-year-old "voluntary" limit on the export of automobiles to the American market. A White House briefer said there was no intention on the U.S. side to bring that up, reportedly because of legal constraints on discussion of such a trade restriction.

In his discussion with The Post, Nakasone would say of the automobile issue only that he "would like to see a continuation of negotiating efforts." The current limitation on the export of Japanese cars to the United States, at the level of 1,680,000 automobiles per year, expires at the end of March. The U.S. auto industry is seeking a two-year extension of the limits, at lower levels, in view of the depressed American automobile market.

Japanese officials said Reagan made no specific plea to Nakasone to open the Japanese market to additional imports of American beef and citrus fruit, but that Secretary of Agriculture John R. Block appealed in the White House meeting for "dramatic steps" along these lines.

Nakasone responded that public pressure from the United States had made Japanese farmers tense and generated a domestic outcry, according to the Japanese sources. He reportedly said future import adjustments for beef and citrus should be discussed by experts of the two countries after an unspecified "cooling-off period."

In responding to Post editors, the Japanese leader said that in view of forthcoming elections in Japan this spring and summer, "I cannot commit myself to liberalization at this moment." This suggested that the U.S. requests in these fields are not likely to be met for at least six months.

Nakasone, 64, has long been one of the most forceful, direct and controversial of Japan's postwar political leaders. His longstanding ambition to be prime minster was frustrated for many years because his rivals distrusted him and by bouts of political maneuvering that seemed always to leave him just short of gaining power.

He finally came to power Nov. 26 after an intense struggle within the ruling Liberal Democratic Party, and with the crucial backing of former prime minister Kakuei Tanaka, who is currently on trial in Japan in connection with the Lockheed bribery scandal.

Nakasone told the Post editors that the public prosecutor's final recommendation in the Tanaka case, scheduled to be announced a week from today, "will be a very disturbing element" in the Japanese Diet, or legislature.

Referring to the grave economic and political dangers facing Japan today, Nakasone compared himself in the talks with Reagan to "a short-term relief pitcher" who had been called into an important baseball game with the bases loaded and no outs. "He must be careful of each pitch, or he'll be knocked out of the box," Nakasone said, according to Japanese officials.

Reagan responded, the officials said, by recalling one of his most celebrated film roles, that of baseball's famous pitcher, Grover Cleveland Alexander, in the 1952 drama, "The Winning Team," co-starring Doris Day. Reagan said that he, too, had been called into the game with the bases loaded against him and that he could only "do my best" to work his way out of danger.

Reagan's reference to the film role appeared to mystify Japanese officials, who told Tokyo reporters that the president had compared himself with "Cleveland Alexander."

The president and his senior aides praised Nakasone for unusually strong action he has taken in the economic and military fields since assuming office seven weeks ago, but at the same time asked the Japanese for greater efforts in the months ahead.

Nakasone's directness in endorsing expanded military missions for Japan was not expected by U.S. officials. In addition to mentioning his aim of counteracting the Soviet Backfire bomber, Nakasone was reported reliably to have endorsed in the White House talks the previously established Japanese objective of patrolling the sea lanes near the home islands.

In order to monitor and stop overflights by the Backfire, Japan would require a much greater radar capability as well as greatly expanded interception capacity, according to U.S. experts. The Japanese will soon acquire a limited number of F15 warplanes, but the number on order is considered insufficient for this task.

To blockade the Soviet fleet in the Sea of Japan would require a much larger number of mines and much more advanced mine-laying air and sea craft than Japan now possesses. Such intentions, to say nothing of capabilities, would present a serious problem for Soviet naval forces and would be likely to generate new protests and pressures from Moscow.