The euro edged down towards $1.12 as the dollar gained the upper hand, thanks mostly to safe-haven demand amid rising tensions in the Middle East.
The Swiss franc hit a new two-year high against the euro, touching 1.1010 francs per euro. The Swiss currency has benefited from investors looking for a refuge from worries about the euro zone economy.
Data published last week indicated that investors remain net long of dollars, unchanged from the previous week, with the U.S. currency having weathered rising expectations for interest rate cuts from the Federal Reserve relatively well.
Currency markets have been stuck in narrow trading ranges in recent weeks, with expectations for easing by both the Federal Reserve and the ECB more or less cancelling out the impact on the euro and the dollar.
Pricing for a 50-basis-point Fed cut soared last week after a dovish speech by New York Fed President John Williams. Those expectations later dwindled after a Fed spokesman clarified that the remarks did not refer to "potential policy actions".
Priced-in forecasts for a 50-basis-point cut have dropped from as high as 71% last week to 18.5% on Monday, with a 25 bps cut now seen as more likely.
"FX markets don't tend to get too excited about monetary policy when it's all nuance and forward guidance, but when central banks are making actual rate moves and QE adjustments, monetary policy becomes the driving theme," BMO Capital Markets strategist Stephen Gallo said.
The Fed holds its monetary policy meeting next week, as does the Bank of Japan.
The euro nudged lower to $1.1217 after earlier reaching $1.1208. The dollar index rose 0.1% to 97.203.
Analysts said the dollar was benefiting from geopolitical tensions surrounding a confrontation in the Strait of Hormuz, the oil trade's most important waterway.
The dollar rose 0.1% against the yen to 107.89 after earlier breaching the 108 level.
Despite the dollar's recent resilience, some analysts think the U.S. currency is set for a fall.
"The USD looks to have peaked. We see medium-term downside on narrowing interest rate differentials and relative growth prospects that could be accelerated by U.S. intervention to weaken the currency," Citi analysts wrote in a research note.
"We anticipate a modest appreciation of the EUR over the longer term, but considerable risks exist if QE (quantitative easing) is accelerated."
Sterling weakened again, falling 0.3% to $1.2469 after Alan Duncan, a British minister and longstanding critic of Boris Johnson quit, decrying the "dark cloud" of Brexit. Johnson is expected to win a Conservative party leadership contest and be appointed prime minister this week.
The pound was also 0.3% lower against the euro, at 89.995 pence.