Japanese Prime Minister Takeo Fukuda said yesterday that he proposed to President Carter the establishment of a Japanese-American fund to support scientific research - particularly in the energy field.

An aide to Fukuda said Carter was generally sympathetic to the idea, but the aide stressed that Carter had not been presented with a detailed plan. Fukuda has in mind a fund with total capital of between $500 million and $1 billion, the aide said.

"I should like to suggest nuclear fusion and solar energy as particularly useful areas for joint R & D," Fukuda told a luncheon hosted by the Japan Society and the Foreign Policy Association.

Enormous technical problems remain before nuclear fusion (the type of reaction that occurs in a hydrogen bomb) can be safely controlled to produce energy.

A colossal financial investment will be necessary, and one of the benefits the Japanese leader sees in joint effort is the elimination of duplication of research and testing. Other nations could join the fund if they chose, Fukuda said.

Fukuda, noted that it is appropriate for Japan and the United States to take the lead in exploring development of energy from new sources because Japan is second to the United States as an importer of oil, a nonrenewable resource.

The Japanese prime minister noted that his nation remains particularly aware of the dangers of nuclear weapons because it was the target of the only two nuclear attacks in history. He stressed the importance of developing safe nuclear power for the future, however.

The luncheon attracted a turnout of about 1,300 in the New York Hilton Hotel's grand ballroom, a reflection of the number of New Yorkers who do business with Japan.

Except for his proposal of a joint fund, however, Fukuda gave the audience only a recapitulation of the points already made public of his talks with Carter and U.S. officials in Washington.

He was reassured by his Washington talks that the United States "sustains its deep interest in Asia," Fukuda said. Washington must continue to demonstrate an interest in Asia in order to dissipate Assian anxieties, he said.

Fukuda also pledged that Japan would continue to improve the terms and increase the size of its foreign aid, once a sore subject because Japan gave so little to developing nations.

Fukuda will end his visit to the United States today and will depart from New York's Kennedy Airport.