UPDATE 1-U.S. concerned at Turkey-Israel rift - Gates

* Defense Secretary concerned at breakdown in ties

* Says Europe a factor in Turkey's shift 'eastward'

(Adds quotes)

LONDON, June 9 (Reuters) - U.S. Defense Secretary Robert Gates voiced concern on Wednesday about Turkey's breakdown in relations with Israel and signs that Ankara -- pushed, he said, by some in Europe -- may be drifting "eastward".

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

"I think 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 reestablished," he added.

Relations between Israel and Turkey broke down after a deadly Israeli raid on an aid flotilla bound for the Hamas-ruled Gaza Strip, but Gates attributed the broader shift by Turkey to European reluctance to accept the country.

"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."

Turkey has been seeking for decades to join the European Union.

Gates said the United States and its European allies need to "think long and hard about why these developments in Turkey (occurred) 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." (Reporting by Adam Entous; Editing by Mark Trevelyan)