The U.S. dollar drifted higher against its most major counterparts in the European session on Tuesday, as investors awaited the release of U.S. jobs data for September that could bolster hopes for a move towards tapering by November.

Friday's nonfarm payrolls data is likely to show a continued improvement in the labor market, with economists forecasting a rise of 488,000 jobs. The jobless rate is seen falling to 5.1 percent from 5.2 percent.

Market participants hope that the Fed would begin to reduce its asset purchases as soon as November following a hawkish statement from the Fed after its meeting in September.

Hopes for an imminent tapering have lifted U.S. bond yields last week, with the 10-year treasury yield surpassing 1.56 percent.

St. Louis Fed President James Bullard reiterated on Monday that high inflation is unlikely to fall back to the Fed's 2 percent goal, but businesses and consumers have adjusted their mentality around inflation.

The greenback rose to 1.1590 against the euro, 0.9271 against the franc and 111.26 against the yen, after falling to 1.1622, 0.9239 and 110.83, respectively in early deals. The greenback may challenge resistance around 1.13 against the euro, 0.94 against the franc and 113.5 against the yen.

In contrast, the greenback retreated from an Asian session's high of 1.3584 against the pound, with the pair trading at 1.3627. The greenback is seen locating support around the 1.38 level.

The greenback fell to 1.2586 against the loonie, 0.6971 against the kiwi and 0.7294 against the aussie, off its prior highs of 1.2630 and 0.6928 and a 4-day high of 0.7249, respectively. The greenback may test support around 1.22 against the loonie, 0.71 against the kiwi and 0.74 against the aussie.

Looking ahead, U.S. and Canadian trade data for August and ISM non-manufacturing PMI for September will be out in the New York session.

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