Oil prices fall after hitting 2015 highs

* Prices hit 2015 highs after first U.S. stock draw since Jan

* Markets remain well supplied despite strong demand

* OPEC indicates it will not cut output alone

SINGAPORE, May 7 (Reuters) - Oil prices fell on Thursday morning in Asian trading after hitting 2015-highs in the previous session as traders moved to take profits on a multi-week rally.

The first drawdown in U.S. crude inventories since January as well as a weakening dollar had fed the oil price rally.

The jump in oil prices has been supported by stronger-than-expected demand growth and a slowdown in crude supply, yet traders said that global crude markets remained well supplied, prompting many to sell contracts to cash in on the recent rally.

OPEC comments made overnight also indicate that core Gulf oil producers are not wavering in their strategy to focus on market share rather than cutting output alone, suggesting big policy changes are unlikely at the June meeting unless non-OPEC producers change their stance.

As a result, benchmark Brent crude futures were trading at $67.25 per barrel at 0033 GMT, down 52 cents since their last settlement. U.S. WTO crude was down 48 cents at $60.45 a barrel.

“Weaker sentiment was also driven by comments from Iran’s oil minister, who indicated its output would increase to 3.8 million barrels per day within six months if sanctions were lifted,” ANZ bank said in a note.

India reached a deal on Wednesday to develop a strategic port in southeast Iran despite U.S. pressure not to rush into any such trade agreements before world powers clinch a final nuclear accord with Tehran. (Editing by Joseph Radford)