Prime Minister Yasuhiro Nakasone swept through Washington this past week, promising that he would deliver where other Japanese prime ministers, by his own evaluation, have failed. At the end of two days of meetings with President Reagan and other officials, Nakasone had them convinced they had met a new style of Japanese leader.

He scored a bull's-eye at the White House. An enthused Ronald Reagan stuck his head out of the Oval Office meeting with Nakasone to tell his private secretary: "Tell Nancy we're going to have guests for breakfast tomorrow ."

To be sure, some Japan-watchers had a sense of de'ja vu: Wasn't Nakasone merely repeating old promises of friendship and cooperation, and pledges that economic and trade frictions would be defused?

Yet, one comes away from a Washington Post breakfast for the tough, 64-year-old veteran Japanese legislator with the feeling that a turn of events, promising a stronger U.S-Japanese working relationship, may be at hand. This Japanese prime minister, no shrinking violet, views himself as a world leader--the head of a major power with international responsibilities, a role his predecessors were not ready to play.

He sees the need, as he said last Sunday on ABC's "This Week with David Brinkley," for a U.S.-Japanese relationship that is "going to last for another thousand or two thousand years." Interestingly enough, the White House picked up the long-term theme after Nakasone and Reagan met. A spokesman cited the need for a relationship lasting through the next century.

Above all, what Reagan and Nakasone were able to agree on, and make known to the world, is that Japan and the United States are important friends--not enemies--who can see beyond the immediate trade problems between them. Nakasone even risked political sniping at home to refer to a Japanese-U.S. "alliance."

Significantly, Nakasone committed Japan, in his administration, to put "political limits" on Japanese economic expansion, to take bolder steps to meet defense responsibilities, and to follow "a new role" in international cooperation. "This is the direction that preceding prime ministers have all sought, but too often their deeds have not matched their words," Nakasone said.

He sounds like, and acts more like, a hustling American politician than the stereotype of the overly humble Japanese premier playing junior partner to his American seniors.

In Japan, his detractors refer to him as a "weather vane," suggesting that he shifts easily in the political winds. But in the best Lyndon Johnson tradition, Nakasone defines pragmatism as a plus, rather than a minus. "All great statesmen are opportunists," he responds to critics.

At the Post breakfast, Nakasone compared the mood that brought him to power to the demand for "stronger leadership" illustrated in the United States by President Kennedy's election following Eisenhower, and President Reagan's election over Carter.

But smiling, sensing the need for a small injection of modesty, Nakasone quickly added: "I'll be frank; I am not so strong a leader as President Reagan."

In deciding to place some limits on economic expansion, Nakasone will be taking on Japan's powerful, free-market-oriented business and banking community. But he plainly feels that there is a more important and larger relationship than mere trade balances.

"We started expanding economically and because of that expansion we are risking ourselves being isolated from the rest of the world," Nakasone said with emphasis. Of course, he's not proposing to cut off economic growth, but he wants to make sure that Japan pursues its growth "without causing adverse repercussions on the rest of the world."

Nakasone will try to establish Japan's--and his own personal--prestige at the Economic Summit meeting among heads of state at Williamsburg, Va., later this year. He believes his predecessors for the most part have tried to stay out of the limelight, preferring to avoid what is crudely referred to as "Jap-bashing."

If Nakasone means it--and isn't tossed on the discard pile by the Japanese establishment--the attitudinal change alone could go a long way toward meeting some of the standard complaints about Japan. He will have to sell the Diet, Japan's national legislature, on his notion of political limits to economic expansion. As in other issues, he's far out in front of the bureaucratic consensus in Japan, which shrinks from international involvements.

Opening up the Japanese market, which Nakasone endorses, and other policy changes, will need legislative approval, as would be the case in any democracy. Having scored well in Washington, Nakasone's leadership now faces its real test in Tokyo.