* Dollar index hits highest since late May
* Sterling slides after BoE's Carney's rates signal
* Fed's Dudley says wages, inflation should pick up
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Jemima Kelly
PARIS, June 20 (Reuters) - The dollar hit a three-week high on Tuesday, boosted by comments from the U.S. Federal Reserve bolstering expectations that it would keep raising interest rates, as sterling skidded on the opposite message from the Bank of England.
The British pound fell almost a cent against its U.S. counterpart after BoE Governor Mark Carney said now was not the time to raise UK interest rates. Last week three BoE policymakers had voted in favour of a hike.
But Carney warned of weak wage growth and a likely hit to incomes as Britain prepares to leave the European Union, sending sterling to a one-week low of $1.2661.
Conversely, New York Fed President William Dudley said on Monday that tightening in the U.S. labour market should help drive up inflation, reinforcing the message that a recent patch of weak data is unlikely to derail plans to keep raising interest rates, after two hikes so far this year.
The dollar index - which measures the greenback against six other major currencies, including sterling - climbed to 97.648 , its highest since the end of May.
"Although Dudley displayed optimism over the health of the US economy, I feel the macro-fundamentals from the States need to display ongoing signs of stability before investors adopt a similar school of thought," said FXTM analyst Lukman Otunuga, in Cyprus.
Separately, Chicago Fed President Charles Evans said on Monday it may be worthwhile for the U.S. central bank to wait until year-end to decide whether to raise interest rates again, but this appeared to have little negative effect on the dollar.
"Bill Dudley commonly represents the majority view on the FOMC (Federal Open Market Committee) - this is the main reason why the dollar is appreciating," said Commerzbank strategist Thu Lan Nguyen, in Frankfurt. "Evans was more dovish but he's known to be dovish."
Investors are now pricing in around a 50 percent chance that rates will be raised again by the end of the year, according to CME FedWatch.
Against the yen, the dollar rose to as high as 111.90 , its strongest level since May 26. That marked a gain of almost 3 percent from the dollar's near 2-month low of 108.81 yen set on June 14.
The greenback has edged higher since the Fed on June 14 raised interest rates for a second time in 2017 and announced it would begin cutting its holdings of bonds and other securities later this year, while indicating that a recent softening in inflation was seen as transitory.
The dollar may see further gains against the yen, especially after Bank of Japan Governor Haruhiko Kuroda last week indicated the BOJ would be in no hurry to dial back its massive stimulus programme, said Tan Teck Leng, forex analyst for UBS Wealth Management in Singapore.
The euro was flat at $1.1144, close to a three-week low.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Additional reporting by Masayuki Kitano in Singapore; Editing by Andrew Heavens and Hugh Lawson)