JERUSALEM, July 23 (Reuters) - Israel will return the Turkish aid ships on which its troops killed nine activists in May, Israeli officials said on Friday, in what appeared to be a new bid to repair frayed ties with its former ally.

Turkey, once a rare Muslim friend of Israel, withdrew its ambassador and suspended joint military exercises after the May 31 raid on the ships taking aid to Gaza. Ankara has also demanded an apology, something Israel has resolutely refused.

While Israel lost a powerful ally in the region, Turkey also rallied outraged Arab and Muslim nations and while doing so staked its claim to a leading role in the Middle East under its AK Party government which has its roots in political Islam.

Talks to return the Mavi Marmara cruise ship and the two other flotilla vessels had been held up by Israel's demand that the owners sign undertakings not to mount new aid missions to the Hamas-run Palestinian territory.

A decision was made yesterday to allow the ships to leave without further conditions. Turkey has been informed. They will leave soon, an Israeli official said.

The Turkish embassy was handling discussions on how to retrieve the ships, another Israeli official said, but the embassy had no immediate comment.

Israel admitted errors in planning the high seas seizure but justified the lethal force of its marines, saying they came under club, knife and gun attacks after rappelling down from helicopters. Activists dispute that account.

Though it has resisted Turkish demands for a wider international investigation and a formal apology, Israel has pursued fence-mending talks. It has also eased overland trade to Gaza, many of whose 1.5 million Palestinians are aid-dependant.

Israel also lifted an advisory on Tuesday against its citizens visiting Turkey, citing fewer protests that might have endangered them. Defence Minister Ehud Barak voiced hope that renewed Israeli tourism to Turkey would improve relations.

Asked why Israel no longer sought formal Turkish assurances that the ships would not sail for Gaza again, an Israeli official cited Ankara's rejection of the idea.

There were also legal challenges in negotiating such a deal with the IHH, a Turkish Islamist charity that chartered the Mavi Marmara and which the Jewish state has designated a terrorist organisation, the official said. (Writing by Dan Williams; Editing by Jon Hemming)