The dollar index, which measures the greenback against six major peers, fell 0.17 percent to 106.4360.
In late New York trading, the euro increased to 1.0190 U.S. dollars from 1.0178 dollars in the previous session, and the British pound increased to 1.2072 U.S. dollars from 1.2067 dollars in the previous session. The Australian dollar was up to 0.6980 U.S. dollars from 0.6912 U.S. dollars.
The U.S. dollar bought 134.86 Japanese yen, lower than 135.06 Japanese yen of the previous session. The U.S. dollar was down to 0.9561 Swiss franc from 0.9618 Swiss franc, and it fell to 1.2863 Canadian dollars from 1.2935 Canadian dollars.
The July U.S. consumer prices index (CPI), a key gauge of inflation, is slated for release on Wednesday.
Headline CPI, which includes energy and food, is expected to dip to 8.7 percent from June's reading of 9.1 percent, according to Dow Jones estimates.
While lower gas prices in July may result in lower headline inflation, the Federal Reserve "won't be impressed by one month of relief, especially if the rate remains north of 8 percent," Chris Low, chief economist at FHN Financial, said in a note on Monday.
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