LONDON, July 8 (Adrian Croft/Reuters) - Turkey would be entitled to take any measure to protect its citizens' rights if Israel fails to apologise or accept an international inquiry into its raid on a Gaza-bound aid ship, Turkey's foreign minister said on Thursday.

If Israel wants to improve relations with us, then they should accept their accountability and do all the necessary actions to prevent deterioration of our relations, Foreign Minister Ahmet Davutoglu told a news conference in London.

The Israeli navy stormed an aid flotilla heading for Gaza on May 31, killing eight Turks and a Turkish-American on board a Turkish ship. Israel said its commandos acted in self-defense.

Davutoglu was quoted on Monday as saying Ankara would cut ties with Israel unless it apologized or accepted an international investigation. But a Turkish government official later told Reuters the minister's words had been misrepresented.

Asked to clarify Turkey's stance, Davutoglu said: We expect Israel either to apologize and to accept these crimes or to accept international investigation.

If they do not follow these two alternatives then of course Turkey ... has full rights to take any measure to protect the rights of ... citizens, he said after talks with British Foreign Secretary William Hague.

Whatever is needed for this, we will take any option, he said, without elaborating.

Israel has said it has no intention of issuing a formal apology to Turkey and has rejected calls for an international inquiry. It has set up a commission headed by a retired Israeli Supreme Court judge and including two non-voting foreign observers to investigate the incident.


DOWNWARD SPIRAL

Once close relations between Israel and Turkey, both U.S. allies, have been on a downward spiral since Prime Minister Tayyip Erdogan spoke out against an Israeli offensive in Gaza at the end of 2008. They soured further after the Israeli raid on the aid ship.

Turkey has said it wants Israel to apologize for the raid, pay compensation, agree to a UN inquiry and lift the blockade of 1.6 million Palestinians living in the Gaza Strip.

Hague's talks with Davutoglu are part of a drive by Britain's new coalition government to build closer trade and investment ties with emerging economies to help boost Britain's recovery from a deep recession.

Afghanistan, Iran, the Middle East peace process, the Western Balkans and Cyprus were on their agenda, Hague said.

Turkey is one of the countries with whom we believe elevated ties are strategically highly desirable for the United Kingdom, Hague said, adding Prime Minister David Cameron hoped to make an early visit to Turkey.

He said Britain and Turkey would conclude a new strategic partnership soon, setting the stage for closer cooperation on foreign affairs, security, defense and trade.

Turkey's negotiations to join the European Union are going slowly and President Abdullah Gul told Reuters this week some of the EU's 27 members were erecting artificial obstacles to Turkish membership.

Hague said Britain strongly supported Turkey's bid to join the EU. This government is clear that for the EU to turn its back on Turkey would be an immense strategic error, he said. (Editing by Janet Lawrence)