In late New York trading on Monday, the euro fell to $1.0729 from $1.0844, and the British pound dipped to $1.2491 from $1.2597, Xinhua news agency reported.
The Australian dollar declined to $0.7540 from $0.7543.
The dollar bought 108.42 Japanese yen, higher than 106.77 yen in the previous session. The dollar inched up to 0.9985 Swiss francs from 0.9889 Swiss francs, and it climbed to 1.3560 Canadian dollars from 1.3537 Canadian dollars.
With no major data due Monday, investors were accessing the US economic prospects under a Trump administration.
Analysts said that the rising possibility of tax cuts and a generally pro-growth set of policies from Trump, aided and abetted by the Republican clean sweep of congress, raised market speculation for a revival in inflation as well as more rate-hikes in the future.
Moreover, Fed Vice Chairman Stanley Fischer said in the previous session that he expects US rates to rise gradually.
He added the US central bank is close to achieving its dual mandate, according to the CNBC.
Early this month, the Fed left interest rates unchanged amid uncertainty about market reactions to the outcome of the US presidential election, but signaled that it could raise rates again as soon as December.
The dollar index, which tracks the greenback against six major peers, was up 1.05 per cent to 100.100 in late trading on Monday, the highest in 11 months.