Japanese Prime Minister Noboru Takeshita presented his country yesterday as a nation that has made major shifts in its economy to bring it more in tune with the rest of the world.

"In a very real sense, we have undertaken to make Japan a nation contributing to the world. We are embarking on this course upon our own will and initiative, and not merely responding to the requests of others," he told the National Press Club in the only public appearance of his three-day Washington visit.

While other Japanese leaders have made that claim before, Takeshita, in his first visit here since becoming prime minister two months ago, stood solidly on the foundation of figures showing an economy that is booming as the result of a buying binge by the Japanese. Included in this boom is a surge in imports, largely Western European luxury goods and manufacturing components from neighboring Southeast Asian nations.

But the import boom has skipped the United States, and trade frictions still loom large in the relationship between the world's two economic powerhouses.

Nonetheless, with the recent economic success story and the announcement of increased contributions for the upkeep of American forces in Japan, Takeshita was able to keep the spotlight off the serious and nagging trade problems that still cloud U.S.-Japan relations.

Trade disputes seemed to play a smaller role in this visit than they did during the farewell trip last May of his predecessor, Yasuhiro Nakasone. That trip was marked by a frenzy of efforts by Japanese officials to persuade President Reagan to lift semiconductor trade sanctions as a parting present to Nakasone and by a private rebuff to the outgoing prime minister's desire to address a joint session of Congress.

Those sanctions still have not been lifted completely, but the issue hardly surfaced this week.

Instead, Takeshita was able to keep attention focused on the larger economic picture, especially the turnaround in the Japanese economy that produced a 3.7 percent growth rate last year and is expected to achieve a slightly greater expansion in 1988 -- despite a doubling in the value of the yen relative to the dollar over the past three years.

Takeshita predicted that his country's restructuring would cut Japan's $82 billion global trade surplus by $10 billion this year -- a figure Reagan administration officials said is not enough.

Takeshita pointed out that the need to integrate Japan's booming economy more closely with the rest of the world was underscored by the global stock market collapse last October and the wild currency swings that followed. "The shock caused people to wonder whether structural imbalances and unrest in financial and currency markets would trigger world economic turmoil," Takeshita said.

Takeshita, furthermore, seemed well on his way to gaining the major objective of his visit -- the forging of close ties with Reagan similar to the first-name relationship that prevailed between the president and Nakasone. Following a custom established with Nakasone, Reagan arranged for an unscheduled meeting with the prime minister yesterday afternoon -- an invitation to Takeshita and his wife to have tea with the president and Mrs. Reagan in their private quarters at the White House.

Japanese diplomats had been concerned over how the president and the American people would react to Takeshita -- an accomplished politician in Japan's consensus-building society who is seen as lacking the flair that made Nakasone popular here. The press club appearance was considered crucial to giving the prime minister the proper image, and Japanese diplomats rehearsed Takeshita for hours yesterday morning with the toughest questions they could come up with.

But none of the press club questions was as hard hitting as those tossed by the diplomats, and Takeshita handled them with sharp, snappy answers and an occasional touch of humor. "Only God knows" was his rejoinder to a question about the correct yen-dollar relationship. The answers were also vague, making no specific promises, as is Takeshita's style.

The sourest note of the visit came with the rejection yesterday by U.S. Trade Representative Clayton K. Yeutter of Takeshita's major trade initiative -- a proposal to grant U.S. engineering and construction companies limited access to $60 billion in planned Japanese public works projects.

"Our preliminary judgment is that the proposal ... does not meet our needs," Yeutter said in a radio interview, in which he suggested that the Reagan administration might have to impose retaliatory sanctions to force a greater opening of markets by Japan. In a law that Reagan signed last month, Congress ordered a ban on Japanese companies getting federally funded U.S. construction contracts as long as American firms face barriers to Japanese public works projects.

Despite the new internationalization of the Japanese economy and the good words that accompanied Takeshita's visit, it is clear that continued trade frictions are having a corrosive effect on the United States' relationship with what a senior administration official described as "our most important ally and economic power in the Pacific." This is especially true in Congress, where lawmakers are aware that their constituents suffer because of Japanese exports and import barriers. It is also obvious among Reagan administration officials who have to negotiate market-opening moves.

And with little narrowing in sight for Japan's $60 billion trade surplus with the United States despite the rise in the value of the yen, makers of American trade policy are likely to continue to face the question that then-U.S. trade representative William E. Brock confronted five years ago:

"What happens," Brock mused after Nakasone paid his first call as prime minister on Reagan, "if and when the Japanese government does everything we've asked them to do, and things don't change that much?"