LONDON, June 9 (Reuters/Adam Entous) - The United States is concerned at a breakdown in Turkey's relations with Israel and fears Europe's rebuff of Ankara's EU aspirations is pushing the pivotal country eastward, Defence Secretary Robert Gates said on Wednesday.

As NATO's only Muslim member, Turkey has been a key U.S. ally in the Middle East, but its deteriorating ties with Israel and recent overtures to Iran have stoked worries in Washington.

I personally think that if there is anything to the notion that Turkey is, if you will, moving eastward, it is, in my view, in no small part because it was pushed, and pushed by some in Europe refusing to give Turkey the kind of organic link to the West that Turkey sought, Gates told reporters in London.

Turkey's long-running negotiations to join the European Union have slowed to a snail's pace, partly because of disputes over Cyprus but also because the leaders of France and Germany have made clear they do not want the Turks to join.

Relations between Ankara and Israel plunged to their lowest level in decades last week after nine Turks were killed when Israeli commandos stormed a Gaza-bound aid flotilla, sparking an international outcry.

At the same time, Turkey has pursued a rapprochement with Iran, promoting a compromise on Tehran's nuclear programme that it believes should avert further international sanctions, which Turkish leaders have publicly opposed.

The Islamist-leaning Turkish government backed the attempt by pro-Palestinian activists to use the convoy of aid ships to break Israel's blockade of the Gaza Strip, controlled by the Islamist Hamas movement.

Prime Minister Tayyip Erdogan responded by recalling Turkey's ambassador from Israel and canceling joint military exercises with the Jewish state.

The deterioration in the relationship between Turkey and Israel over the past year or so is a matter of concern, Gates said.

The two had a pretty constructive relationship and one that contributed to stability in the region, and I hope that, over time, that kind of constructive relationship can be re-established.

He appeared to blame the estrangement more on European obduracy than on Israeli behaviour.

We have to think long and hard about why these developments in Turkey (are occurring) and what we might be able to do to counter them and make the stronger linkages with the West more apparently of interest and value to Turkey's leaders, he said.

An aide to Gates said Washington's concerned included a perception that EU countries were setting the bar higher for Turkey than for past candidates for membership in a deliberate effort to make accession more difficult.

The 27-nation bloc has frozen negotiations on 13 of the 35 policy areas into which the EU talks are divided -- eight due to Turkey's refusal to open its ports and airports to traffic from Cyprus, and five due to French objections to discussing any item that implies eventual Turkish membership.