The euro rose slightly on Thursday ahead of the European Central Bank's interest rate decision. Traders see a European interest rate cut as a near certainty.
While the dollar fell due to renewed bets on the US Federal Reserve cutting interest rates this year.
The Canadian dollar rose slightly, paring some of the previous session's losses after the Bank of Canada became the first Group of Seven member to cut its key interest rate as expected. It was last at 1.3687 to the dollar.
The euro rose 0.07% to $1.0876 as traders looked ahead to a European Central Bank meeting later in the day for clues on the path of interest rates.
While policymakers have signaled their intent to lower borrowing costs this month, they have remained cautious about how quickly subsequent cuts will occur.
The dollar has been broadly weak, partly due to a weak U.S. labor market that has added to the case for interest rate cuts this year.
Data on Wednesday showed the U.S. services sector returned to growth in May after a brief contraction the previous month, but survey details suggested employment continued to shrink.
Against the greenback, the New Zealand dollar touched a three-month high of $0.6201, while the British pound rose 0.09% to $1.2800. The Australian dollar rose 0.25% to $0.6664.
The dollar index, which measures the greenback against a basket of major currencies, fell 0.14% to 104.10 points.
The yen recovered some of its losses from the previous session and rose 0.4% to 155.50 per dollar.