The U.S. dollar moved up against its most major rivals in the European session on Tuesday, as hawkish comments from Fed officials intensified hopes that the Fed will begin to scale back the bond purchase program in the coming months.

Atlanta Fed President Raphael Bostic said on Monday that the central bank could commence tapering between October and December, or even earlier provided there is another month or two of strong employment gains.

There is substantial progress towards the Fed's goal, Bostic said, adding that July's job numbers were "definitely quite encouraging in that regard."

Bostic and Richmond Fed President Tom Barkin said inflation has already reached the Fed's 2 percent threshold, one of two conditions needed before a rate hike move.

Investors await U.S. inflation data due on Wednesday for more clues on the Fed's policy outlook.

The U.S. Senate is expected to pass $1 trillion bipartisan infrastructure bill later in the day and send it to the House of Representatives for a vote.

Senate Majority Leader Chuck Schumer said that after the vote on the infrastructure bill, the Senate will begin a fresh debate on $3.5 trillion plan aimed at expansion of social programs.

The greenback firmed to near a 3-week high of 0.9226 against the franc, more than 4-month high of 1.1716 against the euro and a fresh 2-week high of 110.55 against the yen, off its previous lows of 0.9190, 1.1743 and 110.22, respectively. Next key resistance for the currency is likely seen around 0.94 against the franc, 1.15 against the euro and 112 against the yen.

In contrast, the greenback weakened to 0.7348 against the aussie, 0.7000 against the kiwi and 1.2555 against the loonie, after rising to near a 3-week high of 0.7316, 1-week high of 0.6969 and near a 2-week high of 1.2589, respectively in early trading. The greenback is poised to challenge support around 0.75 against the aussie, 0.72 against the kiwi and 1.24 against the loonie.

The greenback pulled back from an early 2-week high of 1.3836 against the pound and was worth 1.40. The greenback may locate support around the 1.40 level.

Data from the British Retail Consortium showed that UK retail sales continued to grow in July but the pace of growth slowed.

Total retail sales grew 6.4 percent on a yearly basis in July. At the same time, like-for-like sales were up 4.7 percent.

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