At 1242 GMT, the dollar index was up 0.1% on the day at 91.13. It hit a one-month high earlier in the session.
The Swiss franc hit its lowest since November 2020 against the dollar. Dollar-Swiss has been rising since early January and gained some 3.7% so far in 2021.
It is the short end of the yield curve that has particularly affected the dollar, said Jane Foley, head of FX strategy at Rabobank.
"The market is in two minds at the moment and there’s a bit of a pull and push between these two stories," she said.
"One story is that the Fed’s going to keep interest rates low forever and therefore we’re going to have this movement into higher yield, and the other story is actually no Fed rates won’t be as low forever, in fact the Fed could be one of the first central banks to hike."
Riskier currencies including the Australian and New Zealand dollars recovered some recent losses on Monday.
The Australian dollar was down 0.4% at 0.7797 versus the U.S. dollar at 1243 GMT, after the Reserve Bank of Australia re-committed to keeping interest rates at historic lows.
"We continue to believe, though, that the strengthening global recovery boosted by continued loose monetary and fiscal policies will remain supportive for higher commodity prices and a stronger Australian dollar in the year ahead," wrote MUFG currency analyst, Lee Hardman.
The New Zealand dollar was down around 0.1%, at 0.7261 versus the U.S. dollar.
The euro fell, after top European Central Bank officials sounded alarm over the rises in bond yields.
Policymaker Francois Villeroy de Galhau said on Tuesday that some of the recent rises were unwarranted and that the ECB must push back using the flexibility embedded in its bond purchase programme.
ECB Vice President Luis de Guindos said the ECB had the flexibility to counter any undesired rise in yields.
Market participants said that the ECB and the U.S. Federal Reserve were taking divergent tones on rising bond yields, with the Fed appearing less concerned.
At 1245 GMT, the euro was down 0.2% at $1.20295, having hit its lowest in nearly a month earlier in the session .
Euro zone inflation held steady as expected last month, taking a break in what is likely to be a temporary but sharp spike in consumer prices in the coming months, data showed.
Overnight, China's banking and insurance regulator expressed wariness of the risk of bubbles bursting in foreign markets, and said Beijing is studying measures to manage capital inflows to prevent turbulence in the domestic market.
The U.S. Senate will start debating President Joe Biden's $1.9 trillion coronavirus relief bill this week, Senate Majority Leader Chuck Schumer said on Saturday.
Elsewhere, bitcoin was a touch lower, down 1.7% at around $48,804 at 1248 GMT, having recovered some recent losses in the previous session, with Citi saying the popular cryptocurrency was at a "tipping point" and could become the preferred currency for international trade.
(Reporting by Elizabeth Howcroft; editing by John Stonestreet, William Maclean) ((Elizabeth.Howcroft@thomsonreuters.com; +44 02075427104;))