The service would also require U.S. approval.
JAL is still awaiting U.S. permission to start a Tokyo-Kona service, held up by U.S. demands that Japan allow increased service by U.S.-based carriers.
Japan said it will send a senior Transport Ministry official to Washington next week to try to persuade the U.S. Department of Transportation to begin talks leading to a new bilateral passenger aviation agreement. Jiro Hanyu, counselor in charge of international aviation at the ministry, will visit Washington on Monday.
The United States has said it doesn't want to start negotiating a new agreement until Japan honors what the United States says are commitments already in place in the existing agreement.
Top among them is United Airlines' request for additional flights beyond Japan. United wants to launch a new Osaka-Seoul service.
Japan also is demanding additional U.S. flights that it says Japanese airlines are entitled to under the existing agreement, including the Kona service.
Japan is prepared to take sanctions against the United States if no major progress is made, by rejecting an application for an additional daily Los Angeles-Tokyo service that United wants to begin Thursday, government officials say.
JAL wants to start its Hiroshima-Honolulu service July 4, company officials in Tokyo said.
It expects a steady number of passengers on the route, given that many Japanese from western Japan have settled in Hawaii, the company said.
The airline, which already has 58 flights a week between Japan and Honolulu, had planned to begin the three-times-a-week Kona service on April 1.
Gov. Ben Cayetano has urged both sides in the aviation dispute not to hold Hawaii hostage and to give interim approvals for increased services and then go into negotiations for a long-term agreement.
Kyodo News Service contributed to this report.