By Richard Leong

NEW YORK (Reuters) - The Australian dollar strengthened on Tuesday after the Reserve Bank of Australia kept interest rates on hold and hinted it was in no hurry to ease monetary policy further on signs of reasonably strong economic growth.

Sterling recovered further from three-week lows versus the dollar <GBP=D4> set on Monday after two newspaper polls on Tuesday showed Britons narrowly favor remaining in the European Union. The results stood in contrast to surveys released on Monday showing more voters favored leaving the EU.

The dollar hovered near four-week lows against a basket of currencies as traders speculated when the Federal Reserve may raise interest rates following comments from Fed Chair Janet Yellen on Monday and a weak May jobs report on Friday.

"Strong Aussie growth last week seemingly helped shift the RBA's bias into neutral, while decidedly poor U.S. job growth effectively pulled a near-term rate hike off the table," said Joe Manimbo, senior market analyst with Washington-based Western Union Business Solutions in the Reuters Global Markets Forum.

The RBA as expected kept the cash rate at a record low 1.75 percent, after cutting last month for the first time in a year.

Many traders were disappointed that the RBA statement offered no hints on further easing, which led them to exit earlier bets on an imminent rate cut, sending the Aussie higher.

The Aussie was the biggest gainer among major currencies, hitting $0.7458, its highest since May 6 <AUD=D4>. It was up 1.2 percent at $0.7455. It also rose 1 percent against the yen and the euro <EURAUD=> <AUDJPY=>.

Sterling posted strong gains, rising 0.9 percent at $1.4559 <GBP=D4> after hitting a three-week low on Monday on worries about the outcome of the June 23 "Brexit" referendum.

"Markets see Brexit risk as a fundamental threat to the UK economy, that's why the stakes are so high ahead of the vote," Manimbo said.

Uncertainty about Brexit remained high.

The pound's one-month volatility against the U.S. dollar <GBP1MO=> has surged to its highest since early 2009 during the global credit crisis, Reuters data showed.

On the other hand, the dollar was subdued after Fed Chair Yellen on Monday did not specify on the timing of a rate hike.

The dollar index <.DXY> eased 0.1 percent at 93.811, holding above a near four-week trough of 93.745 set on Monday.

The greenback tumbled on Friday when the government said U.S. employers hired workers in May at the slowest pace in more than five years, quashing near-term rate hike bets.

(Additional reporting by Anirban Nag in London and Lisa Twaronite in Tokyo; Editing by James Dalgleish and Meredith Mazzilli)