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President Reagan and Japanese Prime Minister Yasuhiro Nakasone agreed here Wednesday on the ”urgent need” to resolve a nearly $35 billion U.S. trade imbalance with Japan and pledged to start Cabinet-level talks to ensure progress.

Nakasone promised that Japan will ”make further market-opening efforts” and agreed with Reagan to put Secretary of State George Shultz and Japanese Foreign Minister Shintaro Abe in charge of ”an active joint follow-up effort.”

At a press conference later, Nakasone said the trade imbalance is ”a serious headache for myself.” He said it will command the attention of seven of his Cabinet ministers and a special advisory committee that will include an American.

Reagan said, ”We agreed to work strenuously in the months ahead to open our markets fully and to resist protectionist pressures in both countries.”

Failure to do so, he said, would ”complicate” U.S.-Japanese efforts in other areas.

BUT NO schedules were set for lowering specific trade barriers that are frustrating American companies trying to break into the Japanese markets, and no new meetings were scheduled.

Though their meetings centered on trade problems, Reagan also briefed Nakasone at length on next week`s arms-control talks between Shultz and Soviet Foreign Minister Andrei Gromyko in Geneva.

”I informed the prime minister of my intention to pursue effective arms- reduction agreements with the Soviets seriously and zealously, while pointing out that we believe that some hard bargaining lies ahead,” Reagan said.

Nakasone said he ”fully” supports the President`s effort to resume an arms-control dialogue with the Soviets, and Reagan assured him that he would not accept an agreement that allowed the Soviets to remove nuclear missiles targeted at Western Europe only to aim them at Asia instead.

IN A LATER press conference tailored primarily for a Japanese audience, Nakasone said he was impressed by Reagan`s apparent determination to eradicate nuclear weapons. The United States and Japan, Nakasone said, should look for effective means of verification toward that end.

But Nakasone drew the line on support at the development of Reagan`s Strategic Defense Initiative (SDI), the so-called ”Star Wars” weaponry intended as a defense against incoming missiles.

”What SDI entails is not known at the moment,” Nakasone said. ”We tend to take a very prudent approach to this system.” He said he hopes to be kept informed of the system`s development, and especially of any tests.

Earlier, a senior U.S. official said Nakasone was ”sympathetic” and had ”no objections” when briefed on the $26 billion research program.

AFTER 2 1/2 HOURS of meetings between the leaders, the official briefed reporters, on the condition he not be identified. He said the administration was ”very satisfied with the outcome” of the talks.

He stressed Nakasone`s determination to intensify his efforts to open Japanese markets to U.S. exports, especially in telecommunications, in which U.S. firms could compete vigorously.

The official noted that some Japanese firms already are studying purchases of American-made communications satellites. He said Nakasone assured Reagan that all foreign suppliers will be considered, for example, when the government-owned Japanese telephone agency is turned over to private industry on April 1.

Reagan also pressed Nakasone for market-opening efforts in other key areas of U.S. concern: electronics, including computer software; medical technology and pharmaceuticals; and forest products, such as plywood and paper.

”WE HAVE A very strong commitment from the prime minister” to pursue consultations in these areas at the ministerial level backed up by experts in the fields in each country, the official said.

Asked whether any new trade mechanisms were introduced at the meetings, the official said that Reagan and Nakasone wanted to ”reinvigorate existing mechanisms” at the sub-Cabinet level and that both pointed to a recent report by the private U.S.-Japan Advisory Commission as a good starting point.

No mention was made during the talks about the possible extension of voluntary import quotas on Japanese-made automobiles, he said.

Nakasone also said he and Reagan confirmed that Japan and the U.S. will cooperate even more closely ”for launching the preparations for a new round of multilateral trade negotiations this year.”

THE PRESIDENT flew to Los Angeles early Wednesday after a New Year`s holiday at the Palm Springs estate of millionaire publisher Walter Annenberg. After a session in Reagan`s 30th-floor suite at the Century Plaza Hotel, the leaders had a working lunch and made departure statements before the President left for Washington.

Reagan`s approach was friendly, and Tokyo newspapers have referred to the two leaders as ”Yasu and Ron” because their relationship has become warm in the course of four other meetings in the last two years.

But behind the scenes, a major battle raged within the administration over how tough a line Reagan should take with his guest in view of American industry`s frustration over restricted access to Japanese markets.

The President told reporters during a break that ”we won`t argue. We`re good friends.” Indeed, he declared politely that the entire $114 billion U.S. trade deficit was ”worldwide, due to some of our own economic problems.”

PRESSED ABOUT whether Japan`s stiff tariffs had ”a lot” to do with the nearly $35 billion U.S. trade deficit with that country, Reagan answered,

”No, we`ve made great progress.”

Earlier, however, the President was not as sanguine. He said in a recent interview with the Japanese newspaper Yomiuri Shimbun that ”the sheer size of the deficit has generated growing protectionist sentiment in this country.

”Therefore, I urge the Japanese government and people to move even more quickly to open Japan`s market to competitive foreign products.”

At a briefing here Tuesday evening, a Japanese government official pointed to the strong U.S. dollar as the main cause of the trade imbalance. He said that in the last year, the dollar went from 220 yen to 250, sparking a 45 percent rise in Japanese exports to the U.S.

NINETY-FIVE percent of the increase was in production machinery, integrated circuitry and semiconductors, not consumer goods, said the official, who spoke on condition he not be identified. The increase resulted from the rapid growth of the U.S. economy, a growth that domestic

manufacturers of production machinery could not meet, he said.

”We think we will not see this gross trend repeated ever again,” the official said of the 45 percent increase.

Japan`s overall imports grew in 1984 and are expected to increase more in 1985, he said. To aid this growth, Japan decided last month to accelerate scheduled tariff cuts, the official said.

The official expressed the frustration of some in his government, however, over what he said was the failure of some U.S. officials and businessmen to view the brighter side of U.S.-Japanese relations.

JAPANESE BUSINESS investment in the U.S. now stands at $11 billion and has created 150,000 jobs, the official said. U.S. exports to Japan grew 10 percent last year, he said.

The percentage could be increased if U.S. businessmen intensified their presence in Japan, did more market research to learn the needs of Japanese consumers and made greater use of Japanese government trade channels.