The Commerce Department recommended yesterday that President Reagan relax the remaining trade sanctions imposed on Japan six months ago for violating a semiconductor trade pact by dumping memory chips in other countries at less than their fair market value.

"Our monthly monitoring of semiconductors now shows clear, firm and continuing evidence that third-country dumping has stopped," said Commerce Undersecretary Bruce Smart.

But administration officials added that the Japanese have only "improved slightly" their compliance with another part of the agreement: their pledge to make steady progress in increasing their purchases of U.S.-made chips until they reach about 20 percent of the market. That would double the U.S. market share from the time the agreement was signed in September 1986.

As a result, there is unlikely to be any move to lift the $165 million in trade sanctions imposed for failing to provide added market access.

On April 17 President Reagan ordered that tariffs be doubled on a total of $300 million worth of Japanese television sets, lap-top computers, stereos and other consumer electronic products in retaliation for Japan's failure to live up to the trade agreement. Of that total, $165 million was for the lack of access and $135 million was for third-country dumping.

By selling chips in other countries at below their fair value, Japan gave high-technology companies in those markets an unfair advantage over their American competitors for products that use semiconductors.

At the economic summit in June, Reagan lifted $51 million of the $135 million in sanctions because Japan had shown improvement in reducing third-country dumping. The White House is expected soon to announce the ending of the remaining $84 million of the dumping penalty duties..

The semiconductor sanctions, the first such penalties the United States has imposed on the Japanese since World War II, quickly became a watershed in trade relations between the two countries.

Concern that the sanctions marked the start of a transpacific trade war sent financial and money markets around the world spiraling downward, but the president's action also seemed to show Japan that the Reagan administration meant business in trying to remove unfair trade tactics that block U.S. sales.

Semiconductors are the building blocks of high technology, crucial to computers and telecommunications networks and used increasingly in such common products as wrist watches, automobiles and home appliances. In imposing the sanctions, Reagan said a healthy U.S. semiconductor industry is "essential to America's future competitiveness" and cannot be "jeopardized by unfair trading practices."

In announcing the Commerce Department recommendation, Smart said Japan has assured the United States that it is not "restricting the supply of semiconductors," as representatives of U.S. high-technology firms had charged. The U.S. manufacturers had expressed fears that Japan was trying to sabotage the pact by creating artificial shortages for American users of Japanese chips.

Smart said Japanese officials said "that shortages -- if any -- are solely the result of market demand exceeding Japanese production capacity.

"We also have emphasized to the Japanese that in any case of short supply, it is essential that Japanese suppliers treat U.S. customers equitably and on a nondiscriminatory basis," he added.

Smart said the United States will continue to monitor the agreement to make sure that Japan does not resume dumping in other countries.

To determine that Japan had begun complying with the agreement by stopping its dumping, the Commerce Department examined transactions involving about 18.7 million chips between March and August. The August figures showed that the prices had risen to their fair market value, as were the prices of Japanese chips sold in the United States.