The U.S. dollar fell against its most major counterparts in the European session on Tuesday, after rallying on Federal Reserve Chair Jerome Powell's hawkish remarks on inflation and rate hikes.

Investors await non-farm payrolls report due on Friday, which will provide hints about the possibility of another 75 basis-point rate hike in September.

Economists expect employment to rise by 300,000 jobs in August, after a gain of 528,000 jobs last month.

The unemployment rate is expected to remain unchanged at 3.5 percent.

U.S. treasury yields dropped, with the benchmark yield on 10-year note touching 3.058 percent. Yields move inversely to bond prices.

The greenback edged down to 138.14 against the yen, from a high of 138.77 seen at 6:00 pm ET. The greenback may find support around the 120.5 level.

The greenback fell to 4-day lows of 1.0055 against the euro and 1.1760 against the pound, after rising to 0.9982 and 1.1687, respectively in early deals. The greenback is likely to find support around 1.09 against the euro and 1.23 against the pound.

The greenback touched 4-day lows of 0.6956 against the aussie, 0.6194 against the kiwi and 1.2972 against the loonie, reversing from its early highs of 0.6873, 0.6131 and 1.3025, respectively. The next possible support for the greenback is seen around 0.71 against the aussie, 0.63 against the kiwi and 1.26 against the loonie.

In contrast, the greenback climbed to 0.9723 against the franc, its highest level since July 21. If the currency rises further, it may find resistance around the 1.00 level.

Looking ahead, at 8:00 am ET, German preliminary CPI for August is scheduled for release.

U.S. S&P/Case-Shiller home price index and FHFA's home price index for June and consumer confidence for August are set for release in the New York session.

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