The U.S. dollar rebounded against its major counterparts in the New York session on Tuesday, as Minneapolis Fed President Neel Kashkari suggested that more progress on inflation is needed to support a rate cut.

In an interview with CNBC, Kashkari said he needs to see "many more months of positive inflation data" before he would consider cutting interest rates.

Kashkari, who does not have a vote on the rate-setting Federal Open Market Committee this year, also said he could not rule out raising interest rates if inflation fails to slow.

On the economic front, the Conference Board released a report unexpectedly showing a significant improvement in consumer confidence in the month of May.

The Conference Board said its consumer confidence index jumped to 102.0 in May from an upwardly revised 97.5 in April.

The greenback recovered to 0.9124 against the franc, 1.0855 against the euro and 1.2753 against the pound, from an early 8-day low of 0.9085, near 2-week low of 1.0889 and more than a 2-month low of 1.2800, respectively. The currency is likely to locate resistance around 0.93 against the franc, 1.06 against the euro and 1.24 against the pound.

The greenback climbed to 1.3653 against the loonie, 0.6642 against the aussie and 0.6137 against the kiwi, from an early 1-week low of 1.3614, 6-day low of 0.6679 and more than a 2-month low of 0.6170, respectively. The greenback is seen finding resistance around 1.38 against the loonie, 0.63 against the aussie and 0.60 against the kiwi.

The greenback touched a 5-day high of 157.15 against the yen, up from an early 5-day low of 156.57. Next key resistance for the currency is seen around the 160.00 level.

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