The euro fell as low as $1.2795, its lowest since April 4. It last traded at $1.2826, down 0.4 percent on the day.
Against the yen, the euro was at 132.41, up 0.6 percent.
"The negative deposit rate talk is a threat that the ECB is using to keep the euro lower," said Ian Gunner, portfolio manager at Altana Hard Currency Fund. "I doubt with the Bundesbank on board, the ECB will implement it."
Lowering the deposit rate to negative would make holding euros unattractive and lead to a broad sell-off, traders say.
ECB board members Joerg Asmussen and Benoit Coeure said that monetary policy will remain accommodative, bolstering a view the central bank could use unconventional measures like introducing negative deposit rates in coming months to support the recession-hit economy.
Investors added to favorable bets on the dollar, drawing support from comments by a regional Federal Reserve chief who said the Fed could begin easing up on stimulus this summer.
San Francisco Fed President John Williams said the U.S. central bank could completely exit its easing by the end of the year.
(Read More: Money Could Get Tighter by Summer If Jobs Improve: Fed's Williams)
Although Williams is not a voter this year at the Federal Open Market Committee, his views carry weight as they are often considered close to those of top Fed officials such as Chairman Ben Bernanke and Vice Chair Janet Yellen.
Bernanke and Yellen want to keep monetary policy ultra-loose for a longer period of time, while other policymakers, such as Richmond Fed chief Jeffrey Lacker say the economy's prospects are improving and the pace of asset purchases can be reduced.
"His comments took the market by surprise since he is a dove," said Peter Kinsella, currency strategist at Commerzbank.
"It is a dollar story this year as the U.S. labor and housing markets appear to be recovering. And while we do expect the Fed to be cautious in withdrawing stimulus, the economic recovery should drive the dollar higher," he said.