ISTANBUL, July 21 (Reuters) - Turkey's foreign minister met the leader of Hamas this week in Syria, where they discussed how to heal a rift between the Islamist group and rival Palestinian faction Fateh, Turkey's Anatolia news agency reported.

The state-run news outlet did not elaborate on the report, though Hamas' al Qassam website said Turkey's Ahmet Davutoglu and Hamas chief Khaled Meshaal also discussed how to break the Israeli blockade of Gaza during their talks.

Davutoglu affirmed to Meshaal that Turkey will stand by the Palestinian people until the Gaza siege is lifted, a Palestinian politician with Hamas connections told Reuters in Damascus on Wednesday.

Davutoglu met the exiled Hamas leader on Monday while visiting the Syrian capital for talks with President Bashar al-Assad, the reports said.

The meeting with Meshaal is likely to cause concern to Israel, as Hamas opposes peace moves between the Jewish state and the Fatah faction of Palestinian President Mahmoud Abbas, who is backed by Western powers.

Israel's once close ties with Turkey have deteriorated sharply after a May 31 raid on an aid flotilla by Israeli commandos killed nine pro-Palestinian Turkish activists.

Turkey still wants Israel to apologize for the deaths during the Israeli attempt to stop a civilian aid convoy bound for Gaza on May 31. It also insists Israel compensate the victims' families and submit to an international inquiry into the raid.

In a separate development, Israel on Wednesday lifted an advisory that warned its citizens against visiting Turkey, seeing a reduced risk of violent protests.

Israel defended its decision to storm the flotilla but responded to the international outcry over the deaths by last month easing its blockade of Gaza, allowing in civilian goods but keeping out items it says could be used to make weapons.

The Israeli decision did not ease restrictions that bar most Gazans from leaving the enclave by crossing Israel, though it pledged to streamline the process for issuing permits.

Israel imposed the blockade of the Gaza Strip in 2005 and tightened it in 2007 after Hamas won control of the enclave.

Israeli exit restrictions for Gaza's 1.5 million people have only been lifted in humanitarian cases such as medical emergencies, and many Palestinians in the enclave can only access the outside world by going through Egypt.

Turkey regards Hamas as a key factor in the Middle East peace process since it won elections in Gaza and has urged all parties to talk to the group.

Israel and the United States, along with the European Union, have shunned Hamas as a terrorist organization. But Russia, which is also a mediator in the peace talks, has maintained contact with the Islamist group. (Reporting by Simon Cameron-Moore; Additional reporting by Khaled Yacoub Oweis in Damascus; Editing by Jon Boyle)