The U.S. dollar fell against its major counterparts in the European session on Tuesday, as data showing a slowdown in U.S. manufacturing activity tempered expectations for aggressive monetary tightening by the Federal Reserve.

U.S. treasury yields dropped after weak data, with the benchmark yield on the 10-year note touching 3.58 percent. Yields move inversely to bond prices.

European shares rose sharply as soft ISM manufacturing data raised hopes for slower Fed tightening.

Investors await U.S. non-farm payrolls report due later this week to help determine the central bank's rate hike path in the period ahead.

The greenback weakened to a 2-week low of 1.1429 against the pound and near a 2-week low of 0.9896 against the euro, off its early highs of 1.1280 and 0.9806, respectively. The greenback may challenge support around 1.23 against the pound and 1.09 against the euro.

The greenback edged down to 0.9867 against the franc, from a high of 0.9942 set at 10 pm ET. On the downside, 0.93 is possibly seen as its next support level.

The greenback slipped to an 8-day low of 1.3568 against the loonie, near 2-week lows of 0.6547 against the aussie and 0.5758 against the kiwi, from its prior highs of 1.3653, 0.6451 and 0.5680, respectively. The greenback is seen finding support around 1.33 against the loonie, 0.70 against the aussie and 0.62 against the kiwi.

The greenback pulled back to 144.53 against the yen, from a high of 144.92 seen in the previous session. If the greenback falls further, it is likely to test support around the 121.00 level.

U.S. factory orders for August will be featured in the New York session.

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