Israel no longer trusts Turkey, Erdogan says

* Israel does not want Turkey to mediate with Syria, PM says

* Syria not likely to join French-mediated talks, he says

ISTANBUL, Nov 18 (Reuters) - Israel no longer trusts Turkey to mediate peace talks with Syria, Turkish Prime Minister Tayyip Erdogan said on Wednesday, signaling how much relations have deteriorated between the regional allies in recent months.

Erdogan singled out Prime Minister Benjamin Netanyahu for failing to trust Ankara, unlike his predecessor Ehud Olmert, and also said he did not think Syrian President Bashar al-Assad would accept a French role in mediating with Israel.

Turkey, NATO's only Muslim member, last year facilitated contacts that focused on Syrian demands for a full withdrawal from the Golan Heights -- which Israel captured in 1967 and annexed -- and Israel's accusations that Damascus arms militants in Lebanon and the Gaza Strip.

Those contacts failed to produce formal negotiations, and Turkey's repeated offers to re-open the peace track have not resulted in further talks. Under Netanyahu, Israel has ruled out resuming Turkish-mediated talks with Syria, insisting that any new contacts must be direct.

"On this issue (of mediation), Israel's stance is that it doesn't trust us," Erdogan told a news conference in Rome, where he was attending a U.N. food summit.

"Former Israeli Prime Minister Olmert trusted Turkey, but Netanyahu doesn't trust us. That's his choice," he said in remarks which were televised in Turkey.

Relations between Turkey and Israel have soured since the latter launched an incursion into the Gaza Strip in December.

Erdogan, whose ruling party traces its roots to a banned Islamist movement, has repeatedly criticized the incursion, even having a public shouting match with Israeli President Shimon Peres in January.

Netanyahu and Assad met French President Nicolas Sarkozy separately last week, and Israel said it is ready for talks.

"Now France is trying to take up the role we had," Erdogan said. "I'm not sure what kind of stance Bashar Assad will take, but from what I've heard from him, they're not going to accept something like this."