TOKYO, JULY 6 -- Prime Minister Yasuhiro Nakasone today urged legislators to approve "without delay" a $14.3 billion supplementary budget measure that he said is needed to stimulate the sluggish economy and ease friction with Japan's trading partners.

"Japan can only survive through free trade," Nakasone said. "There can be no prosperity for Japan except in global prosperity, and Japanese growth is contingent upon the revitalization of the world economy."

The remarks by the prime minister, whose term expires Oct. 31, were made in a policy speech to the Diet, or parliament, which convened today for a 65-day extraordinary session.

Nakasone, 69, also raised the thorny issue of tax reform, which stalled the regular Diet session that ended May 27 and prevented smooth passage of the $381 billion main budget this spring, calling the overhaul of Japan's tax system "an absolute imperative."

"We hope to submit the necessary tax legislation to this session of the Diet and to effect income and other tax cuts this fiscal year," he said. "I believe there is a growing popular understanding of this need."

Referring to his pledge to carry out a $43 billion package of emergency economic measures at the Venice summit of industrial nations last month, Nakasone called for the swift passage of the $14.3 billion supplementary budget for fiscal 1987, which began April 1.

The budget is necessary to introduce the economic stimulus package, which government officials hope will help Japan attain a 3.5 percent economic growth target for the current fiscal year, up from 2.5 percent last year.

"While the Japanese economy is basically sound, there is a continuing sense of malaise centering on the manufacturing sector, and the employment outlook remains grim," Nakasone said.

"While we are already moving ahead on those things that can be done independently, the administration has today submitted a supplementary budget draft for these economic measures to the Diet in the expectation it will be enacted without delay," he said.

The supplementary budget includes $720 million of the $1 billion set aside for imports of aircraft and supercomputers to reduce Japan's global trade surplus, which hit a record $93.76 billion in 1986. The imbalance with the United States alone hit a record $59 billion last year.

In addition, the supplementary outlay contains $12 billion for public works projects, $100 million in loans to African countries and an income tax reduction of more than $7.1 million.

Debate on the budget is scheduled to begin in the powerful lower house of the Diet next week. Approval is almost certain as Nakasone's ruling Liberal-Democratic Party holds a comfortable majority in both houses.

The supplementary budget marks an end to the austere policy pursued by the government to reduce the budget deficit, and will boost the government's spending in the 1987 fiscal year by 4.4 percent over the preceding year.

The current Diet session will be the last one before Nakasone's one-year extended term as LDP president and prime minister expires.

Nakasone, who served two consecutive two-year terms as party president, won an unprecedented one-year extension of his term after the party's historic election victory last year. LDP rules bar a third consecutive term.