* U.S. stocks open higher after six days of losses
* Euro reverses gains after Trichet's comments
* ECB is strongly vigilant on inflation -- Trichet (Updates with ECB's Trichet comments, updates prices, adds comment, changes dateline, previous LONDON)
NEW YORK, June 9 (Reuters) - The euro fell against the U.S. dollar on Thursday after the chief of the European Central Bank signaled an interest-rate increase next month as had been widely expected, while U.S. stocks rebounded after six days of losses.
The European Central Bank earlier left its benchmark interest rate on hold at 1.25 percent. In a news conference following the decision, ECB President Jean-Claude Trichet said the central bank is strongly vigilant over inflationary pressures.
Investors typically view Trichet's use of the phrase "strong vigilance" as a code word for a pending rate hike by the ECB in the following months. The euro initially rose on the comments, before retreating as analysts said a hike in July had already been priced in. For Trichet's remarks, click on [ID:nFAT007213].
"The July rate hike has been fully discounted and the euro is suffering from a 'sell the fact' price action," said Richard Franulovich, senior currency strategist, at Westpac Securities in New York.
The euro last traded 0.6 percent lower at $1.4483
U.S. stocks opened higher. The Dow Jones industrial average <.DJI> was up 33.90 points, or 0.28 percent, at 12,082.84. The Standard & Poor's 500 Index <.SPX> was up 3.32 points, or 0.26 percent, at 1,282.88. The Nasdaq Composite Index <.IXIC> was up 1.83 points, or 0.07 percent, at 2,677.21. (Additional reporting by Gertrude Chavez-Dreyfuss, Editing by Chizu Nomiyama)