The U.S. dollar climbed against most major currencies on Monday as investors were digesting the latest remarks from Federal Reserve officials.

William Dudley, president of Federal Reserve Bank of New York, said on Monday that factors restraining price pressures should disappear with time, allowing the U.S. central bank to maintain its gradual pace of monetary policy tightening, according to Bloomberg.

Inflation should pick up with "the fading of effects from a number of temporary, idiosyncratic factors," stabilizing around the Fed's two-percent goal over the medium term, he added.

Meanwhile, Chicago Fed President Charles Evans said that he broadly agrees with his colleagues who believe rates should rise gradually to about 2.7 percent over the next two years or so, from the current range of between one percent and 1.25 percent.

But he said inflation, running at 1.4 percent by the Fed' s preferred gauge, is too low, and voiced concerns that low inflation expectations will keep it from rising toward the Fed' s inflation goal.

The dollar index, which measures the greenback against six major peers, was up 0.54 percent at 92.673 in late trading.

In late New York trading, the euro fell to 1.1839 U.S. dollars from 1.1948 U.S. dollars, and the British pound declined to 1.3467 U.S. dollars from 1.3531 U.S. dollars. The Australian dollar decreased to 0.7944 U.S. dollar from 0.7968 U.S. dollar.

The U.S. dollar bought 111.66 Japanese yen, lower than 112.00 yen of the previous session. The U.S. dollar dropped to 0.9674 Swiss franc from 0.9699 Swiss franc, and it edged up to 1.2354 Canadian dollars from 1.2335 Canadian dollars.