Koizumi and French President Jacques Chirac discussed the deadlock over the International Thermonuclear Experimental Reactor (ITER) during talks in Tokyo.
"Japan has no intention to withdraw its bid to invite ITER," Koizumi told a joint news conference with the French head of state.
"With President Chirac, we have agreed to continue our discussions to reach a mutually agreeable solution."
Before Koizumi's remarks, Chirac had said the Japanese leader made proposals on ITER "which seem to be a nature that could allow an agreement."
The project, which would emulate the sun's nuclear fusion, is designed to one day generate inexhaustible supplies of electricity, but is not expected to be operational before 2050.
The European Union has threatened to build the reactor in France unless Japan compromises by July.
The United States and South Korea support Japan's offer to build ITER in Rokkasho-mura, a northern Japanese village near the Pacific Ocean, while China and Russia back the EU bid for the southern French town of Cadarache.
Japan and the European Union reportedly have offered compromises to each other, proposing that one side get the main ITER reactor in exchange for the other hosting supporting research.