Reversing direction, the U.S. dollar fell against its major counterparts in the New York session on Monday, after a data showed that nation's service sector growth slowed more than expected in May.

Survey data from the Institute for Supply Management showed that services PMI fell to 50.3 in May from 51.9 in April. Economists had expected the index to edge down to 51.5.

The currency was higher in the European session as strong jobs data increased the likelihood of the Federal Reserve keeping rates higher for longer.

The Fed is due to announce its latest monetary policy decision next week, with the central bank widely expected to hold the rate at 5.00 percent - 5.25 percent.

The greenback fell to 1.0722 against the euro and 139.25 against the yen, from an early 4-day high of 1.0674 and a 6-day high of 140.45, respectively. The next likely support for the currency is seen around 1.09 against the euro and 137.00 against the yen.

The greenback eased to 0.9056 against the franc and 1.2432 against the pound, off its early 5-day highs of 0.9119 and 1.2368, respectively. The greenback is likely to find support around 0.89 against the franc and 1.26 against the pound.

The greenback dropped to 0.6637 against the aussie and 0.6085 against the kiwi, reversing from an early high of 0.6579 and a 4-day high of 0.6041, respectively. The greenback is seen finding support around 0.68 against the aussie and 0.62 against the kiwi.

In contrast, the greenback moved up against the loonie, touching a 4-day high of 1.3461. The greenback may find resistance around the 1.36 level.

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