* ECB minutes reveal concerns over currency overshoot, sink euro
* Dollar volatile after rumors of Cohn resignation
* Dollar falls vs safe haven currencies
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh (Updates to U.S. market trading, adds data, quote, changes dateline, previous LONDON)
NEW YORK, Aug 17 (Reuters) - The dollar rose on Thursday, boosted by weakness in the euro after the European Central Bank's July policy meeting minutes, but was volatile as rumors swirled about the possible resignation of Gary Cohn, director of the U.S. National Economic Council.
A tweet sent from an unverified news account said Cohn was set to resign. That pared the dollar's early gains against most major currencies and sent the dollar index, which tracks the U.S. currency against six rivals, near its lows on the day.
The greenback recovered modestly after a tweet from a reporter, which cited a source as saying the rumors were "100 percent false."
The White House released a statement shortly after saying Cohn "intends to remain in his position."
That helped calm markets as Cohn, along with Treasury Secretary Steve Mnuchin, is seen as pivotal to U.S. President Donald Trump's economic agenda of tax cuts and infrastructure spending.
The dollar index was last up 0.12 percent at 93.656.
Still, analysts said, the dollar was in an unenviable position with inflammatory news headlines coming from the White House weighing on its already weak position.
"We had yesterdays Fed minutes that certainly didnt do the dollar any favors," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
The dollar fell Wednesday after the release of minutes from the Federal Reserve's July policy meeting that showed policy-makers growing more worried about weak U.S. inflation.
"We have to look at it in that context, where the dollar's already on a somewhat shaky footing," Esiner said. "These latest rumors add to an already negative tone for the dollar."
The dollar index's largest component is the euro, which sank to a three-week low after the release of the ECB's minutes showed officials warning about a possible market overshoot for the currency. The euro has risen close to 12 percent against the dollar this year.
The minutes, released at 7:30 a.m. EDT (1130 GMT), spurred an almost 1 percent fall in the single currency against the dollar along with losses against the Swiss franc, yen and sterling.
The minutes showed rate-setters were highly aware of the risk that the euro could threaten the ECB's efforts to get inflation higher as they decided against any change to their pledge of continued monetary stimulus last month.
The dollar remained lower against most major currencies, particularly the safe-haven Japanese yen and Swiss franc .
(Reporting by Dion Rabouin; Editing by Chizu Nomiyama)