Dollar falls on more unwinding of bullish bets after Fed

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The U.S. dollar fell for a second straight session against a basket of major currencies on Monday after traders unwound bullish dollar positions on the likelihood that Federal Reserve policy will be accommodative over the near term.

The dollar added to its losses against the euro following a Fed statement on March 18 that suggested a less aggressive timetable for hiking interest rates. Last week was the dollar's worst week against the currency since late 2011.

"There's a very large long-dollar position in the market, and what we appear to be facing is an unwind of that position," said Richard Cochinos, head of Americas G10 FX strategy at Citi in New York.

He said the weakness in the dollar could persist and that the euro, which rose over 1.3 percent against the greenback to a session high of $1.09692 on Monday, could hit $1.12 by the end of the week. The dollar's weakness against the euro last week came after it hit 12-year highs against the currency.

The euro continued to strengthen against the dollar despite comments from European Central Bank President Mario Draghi on the central bank's bond-buying stimulus plan. The plan has a weakening effect on the euro.

"With the ECB (quantitative easing) program firmly in place, the euro's sensitivity to ECB rhetoric is likely to be lower," said Vassili Serebriakov, currency strategist at BNP Paribas in New York.

Analysts said failed progress in talks on Monday between German Chancellor Angela Merkel and Greek Prime Minister Alexis Tsipras could lead the euro to give back some gains against the dollar.

Merkel does not expect the talks with Tsipras to resolve Greece's differences with the euro zone over a bailout, but she does want to hear from him in person about his reform plans, an aide said.

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The euro was last up 1.22 percent against the dollar at $1.09517, not far from a nearly two-week high of $1.10625 hit last week. The dollar was last down 0.25 percent against the Japanese yen at 119.73 yen.

The dollar was down 0.95 percent against the Swiss franc at 0.9659 franc. The dollar index, which measures the greenback against a basket of six major currencies, was last down 0.95 percent at 96.98.