* Dollar index hits almost 4-week low during Yellen speech
* Yellen speech fails to increase Fed rate hike odds
* Brexit fears drag sterling to 3-week low (Recasts, updates to U.S. afternoon trading, adds quotes)
By Dion Rabouin
NEW YORK, June 6 (Reuters) - The dollar fell to its lowest in almost four weeks on Monday as Federal Reserve Chair Janet Yellen gave few hints a U.S. interest rate hike is forthcoming following Friday's weak U.S. payrolls report.
The dollar took its largest one-day percentage fall against a basket of major currencies in four months on Friday after the jobs report, which was the weakest in nearly six years.
In a speech on Monday, Yellen sounded a generally upbeat tone, saying that interest rate increases would be forthcoming. But she removed a reference to the timing of the hikes.
On May 27, Yellen said a rate increase could be appropriate in the coming months if the economy and jobs market improved further.
Yellen's statement "was generally more positive than I would have expected given Friday's number, but the fact that she did remove that timeframe I think just suggests that June's off the table" (for a rate hike), said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange.
"July, I think, is still in play but that's going to require upcoming economic data to suggest that the jobs number of Friday was a little bit more of an outlier, not necessarily a trend in slowing jobs growth."
Friday's data showed U.S. non-farm payrolls increased by 38,000 jobs last month. That was the weakest reading since September 2010 and missed a forecast of a 164,000 increase.
The dollar index, which tracks the dollar against six major currencies, fell 0.2 percent to 93.745, its lowest since May 11, during Yellen's remarks. It was last down 0.04 percent at 93.995.
"Some had thought that maybe Yellen would continue to hold a hawkish view, but in reality what could she say? Overall that print was terrible," said John Doyle, director of markets at Tempus Inc. "And with Fed saying that they're data-dependent, you can't have a (jobs report) like that and then expect them to raise rates two weeks later."
U.S. interest rates futures implied traders have all but priced out any chance the Fed will raise rates at its policy meeting next week, Reuters data showed.
Sterling fell more than 1 percent to a three-week low after a number of polls pointed to the "leave" camp ahead of the June 23 referendum on whether Britain stays in the EU.
The pound was 0.4 percent lower at $1.4456 after falling in Asian trade to $1.4352, its lowest since May 16. (Reporting by Dion Rabouin; Additional reporting by Richard Leong; Editing by Dan Grebler)