The U.S. dollar fell against its major counterparts in the Asian session on Tuesday, as the sentiment lifted up after the U.S. House of Representatives backed President Donald Trump's push for increasing the direct payments in the coronavirus relief package and send the bill to the Senate.

The House voted on Monday to increase the stimulus checks to $2,000 from $600 as demanded by Trump.

The bill was headed to the Senate, where Republicans are likely to block the measure due the budget deficit.

But the House voted to override Trump's veto of a $740 billion defense bill that was approved by Congress earlier this month.

Risk sentiment improved as Trump's signing of the Covid aid package raised optimism about an economic recovery.

The greenback weakened to 1.3495 versus the pound, from a high of 1.3439 hit at 5:00 pm ET. The currency is seen finding support around the 1.37 region.

The greenback reached as low as 0.8865 against the Swiss franc, setting a 1-week low. On the downside, 0.87 is possibly seen as its next support level.

The U.S. currency pulled back from its early highs of 1.2206 against the euro and 103.82 against the yen and was trading at 1.2243 and 103.62, respectively. The greenback may test support around 1.24 against the euro and 100.00 against the yen, if it drops again.

The greenback edged down to 0.7599 against the aussie, 0.7124 against the kiwi and 1.2820 against the loonie, following its early highs of 0.7574, 0.7096 and 1.2853, respectively. The currency is likely to target support around 0.78 against the aussie, 0.73 against the kiwi and 1.26 against the loonie.

Looking ahead, S&P/Case-Shiller home price index for October is scheduled for release in the New York session.

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