JERUSALEM, June 5 (Reuters) - Prime Minister Benjamin Netanyahu responded coolly on Sunday to France's proposal to convene Israeli and Palestinian negotiators in Paris, saying the United States might want to pursue an initiative of its own.

We will study the proposal and discuss it with our friend, the United States, Netanyahu told his cabinet, in remarks released by the prime minister's office.

The Americans also want to promote initiatives, and we have our own thoughts, too, he said, without elaborating on possible ways to revive U.S.-sponsored peace talks that fizzled soon after they began last September.

We will see how the (French) proposal fits with other initiatives. Understandably, it's not possible to implement all of them, and it's better to concentrate on one initiative and move it forward, Netanyahu said.

French Foreign Minister Alain Juppe, on a visit to Israel and the occupied West Bank this week, offered to host talks this month or in early July to discuss ideas for a Palestinian state raised last month by U.S. President Barack Obama.

Israel has traditionally been reluctant to embrace a major European role in Middle East peace-making, preferring to have its main ally, the United States, take the lead.

Obama's proposal to use Israel's pre-1967 war frontiers as the starting point for negotiations on a Palestinian state in the occupied West Bank and Gaza Strip, territories captured by Israeli forces in that conflict, has drawn Netanyahu's ire.

Palestinian President Mahmoud Abbas told Reuters on Saturday the French initiative was acceptable in principle and that it relates to Obama's view of the 1967 borders as the basis for statehood talks.

Netanyahu, who met Juppe on Thursday, has said a return to Israel's narrow 1967 frontiers would leave it with indefensible borders. He clashed publicly with Obama over the issue during a tense visit to Washington two weeks ago.

In the absence of peace talks, the Palestinians plan unilaterally to seek U.N. recognition of statehood in September -- a step Israel strongly opposes, fearing it could end up being isolated internationally.

The United States has already said it opposes the plan, and it could veto a recognition bid in the U.N. Security Council. Juppe said that France, also one of the five permanent members of the Security Council, has not yet decided whether to back the Palestinians.

(Writing by Jeffrey Heller, Editing by David Cowell)