The dollar index, which measures the greenback against six major peers, was up 0.19 percent at 93.5485.
In late New York trading, the euro fell to 1.1759 U.S. dollars from 1.1782 dollars in the previous session, and the British pound was down to 1.3074 dollars from 1.3101 U.S. dollars in the previous session. The Australian dollar was down to 0.7119 U.S. dollar from 0.7145 dollar.
The U.S. dollar bought 105.97 Japanese yen, higher than 105.77 Japanese yen of the previous session. The U.S. dollar increased to 0.9178 Swiss franc from 0.9138 Swiss franc, and it rose to 1.3385 Canadian dollars from 1.3384 Canadian dollars.
On the data front, economic activity in the U.S. manufacturing sector grew in July, with new orders and production driving much of the strength, according to the Institute for Supply Management (ISM) on Monday.
U.S. manufacturing PMI (Purchasing Managers' Index) registered 54.2 percent in July, up 1.6 percentage points from the June reading of 52.6 percent, the ISM reported.
Monday's market movement followed a downbeat week that saw the U.S. dollar index dip 1.14 percent.
Downside risks in the greenback remain as a resurgence in coronavirus infections intensifies doubts about a quick recovery of the U.S. economy, experts noted.
"What is decisive for the FX market is the question which countries will emerge from the crisis quickly and well," Esther Reichelt, analyst at Commerzbank, said in a note on Monday.
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