The U.S. dollar depreciated against its major counterparts in the Asian session on Tuesday, as most Asian shares climbed on growing optimism over the passage of a $1.9 trillion stimulus package by the U.S. government.

House Democrats released a draft of stimulus plan on Monday evening, which includes $1,400 stimulus checks, $400 federal unemployment benefits, funding to state and local governments and vaccine distribution among other provisions.

Democrats are rushing to put the stimulus plan for a floor vote by the end of the month. Thereafter, the bill would go to the Senate for approval.

China's central bank pledged a "stable" monetary policy after recent concerns about liquidity squeeze.

In its monetary policy report released on Monday, the PBOC promised to keep monetary policy flexible and precise in order to strike a balance between economic recovery and risk prevention.

The greenback dropped to 1-week lows of 1.2087 against the euro and 0.8956 against the franc, from its prior highs of 1.2044 and 0.8991, respectively. Next key support for the greenback is likely seen around 1.23 against the euro and 0.86 against the franc.

Retreating from its early highs of 1.3732 against the pound and 105.26 against the yen, the greenback fell to near a 3-year low of 1.3788 and an 8-day low of 104.75, respectively. If the greenback drops further, 1.41 and 100.00 are possibly seen as its next support levels against the pound and the yen, respectively.

The greenback slipped to near a 2-week low of 1.2719 against the loonie, 2-week low of 0.7731 against the aussie and near a 5-week low of 0.7255 against the kiwi, easing from its previous highs of 1.274, 0.7697 and 0.7215, respectively. The greenback is seen finding support around 1.25 versus the loonie, 0.79 versus the aussie and 0.74 versus the kiwi.