Trump also faced growing pressure from Republicans to put aside his misgivings and approve the economic relief legislation, "You don't get everything you want even if you are the President of the United States", Sen.
Trump released a statement upon signing the bill, reiterating his demand for $2,000 checks, and said he was sending back a redlined version of the bill to cut wasteful items.
The vote comes a day after Trump signed the relief and government spending bill into law, averting a government shutdown set to begin Tuesday.
While the bill has been signed into law, several of Nevada's unemployment benefit programs expired over the weekend including the pandemic unemployment assistance program, pandemic emergency employment compensation, and state extended benefits.
In a strongly worded statement published on the transition website on Saturday, Mr Biden described Mr Trump's refusal to sign the bill as an "abdication of responsibility".
Trump has not explicitly said he will veto the bill, which passed Congress Monday with big veto-proof majorities.
On Twitter, the president reiterated his objection to the bill, saying: "I simply want to get our great people $2000, rather than the measly $600 that is now in the bill".
Instead, he assailed the bill's plan to provide $600 COVID relief checks to most Americans - insisting it should be $2,000.
That demand also plays into Democrats' hands.
House Speaker Nancy Pelosi, the top Democrat in the lower chamber, brought to the floor a standalone bill that would boost the amount of stimulus checks to 2,000 dollars on Thursday, but Republicans in the House blocked the attempt.
Senator Bernie Sanders said Sunday that "what the president is doing right now is unbelievably cruel". The idea is likely to die in the Republican-controlled Senate.
"In the bipartisan negotiations, Leader [Chuck] Schumer and I repeatedly asked Republicans what would be the highest number the President would accept for direct payments, and they responded with Sphinx-like silence", House Speaker Nancy Pelosi, D-Calif wrote in a letter to her caucus on December 23.
Treasury Secretary Steven Mnuchin said these checks will come more quickly than March's stimulus money for people who used direct deposit.
While Congress will also override the stimulus veto, Trump can simply refuse to sign the bill until the current session of Congress ends and the new session begins on January 3.
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