By Dion Rabouin

NEW YORK (Reuters) - The dollar rose on Tuesday as investors sold the British pound and the euro on news that the gap had narrowed in the latest poll on Britain's referendum on European Union membership.

Both currencies fell against the greenback after a poll showed the percentage of voters supporting Britain's exit from the EU had risen to 44 percent from 42 percent in its previous poll on Sunday. A plurality of respondents still preferred "Remain" but by just a one-point margin, with 45 percent support.

The euro fell further after European Central Bank President Mario Draghi said during a speech at the European Parliament that Britain's June 23 referendum was adding uncertainty to markets, and that the ECB was ready to act with all instruments if necessary. He also said that "further monetary policy stimulus (was) in the pipeline."

That spooked markets, said David Gilmore, partner at FX Analytics in Essex, Connecticut, because many investors misinterpreted Draghi's remarks.

"Markets read that as there’s going to be more quantitative easing or asset purchases on a monthly basis or interest rates are going to be more negative or both," Gilmore said. "That's not what he said. But the move happened and people bought dollars and sold euros on that headline."

The dollar made its biggest gain of the day, against the yen <JPY=>, rising 1 percent to 104.97 yen, in what investors said was a mix of technical positioning and profit taking on Brexit fears.

"The yen has been eerily quiet in recent days," said Axel Merk, president and portfolio manager at Merk Hard Currency Fund in Palo Alto, California. "It clearly has strengthened quite substantially, but as fears eased you should have seen a backing out of yen ... now it’s weakening."

The euro <EUR=> fell 0.5 percent to $1.1255, holding just above a session low of $1.1243.

The dollar index <.DXY>, which measures the greenback against six major world currencies, rose 0.45 percent to 94.031.

Sterling <GBP=> turned negative against the dollar after the release of the Survation poll and fell further during Draghi's speech. It was last down 0.35 percent at $1.4643.

The pound had earlier climbed to its highest against the dollars since early January after the release of two earlier 'Brexit' opinion polls that indicated the "Remain" camp had regained some ground.

(Reporting by Dion Rabouin; Editing by Diane Craft and Steve Orlofsky)