The single currency bought $1.3132 in the morning -- its highest since early May -- compared with $1.3127 late Friday in New York Friday.

The euro was also trading at 102.70 against the yen, from 102.90 yen on Friday, while the dollar was at 78.21 yen from 78.37 yen.

"The dollar fell broadly, dropping to a four-month low versus the euro, after the Fed's Thursday announcement of a third bond-buying programme," Phillip Futures said in a report.

The Fed said Thursday it would start a third programme of bond-buying, or quantitative easing, by purchasing $40 billion a month in mortgage-backed bonds and would keep the scheme in place until it saw substantial improvement in the jobs market.

The measure will see a flood of dollars hitting the market, likely weakening the unit.