The euro zone currency posted its largest gain in a month after Draghi's remarks last Thursday, but has since given up ground against the dollar.
Investors now turn their attention to the U.S. Federal Reserve's policy meeting on Tuesday and Wednesday. The central bank's Federal Open Markets Committee is expected to keep interest rates unchanged.
"It's the combination of a market that overextended in the opposite direction because of Draghi's 'no more rate cut' comment and just some corrective natural price action into the risk of an FOMC that could be a little bit more hawkish," said Richard Scalone, co-head of foreign exchange at TJM Brokerage in Chicago.
Traders will also be watching interest rate decisions from the Swiss, Australian and Norwegian central banks this week, along with the Bank of England and Bank of Japan. Those meetings are likely to provide a test of central banks' ability to successfully manage market expectations, analysts said.
The euro
The dollar rose broadly against major European currencies on Monday. Against the Swiss franc
The biggest moves on the day were in emerging markets where several currencies sold off amid local turmoil. The South African rand
The Brazilian real
The Egyptian pound
The Russian rouble
(Editing by Bernadette Baum and Paul Simao)
By Dion Rabouin