The measure faltered on Sunday after it failed to get the necessary 60 votes in the 100-member chamber to clear a procedural hurdle after days of negotiations.
Senate Majority Leader Mitch McConnell urged Democrats to stop their "obstruction," saying it was delaying aid and hurting financial markets.
The bill is Congress' third effort to blunt the economic toll of the disease.
It envisages financial aid for regular Americans, small businesses and critically affected industries, including airlines.
Democrats had raised objections to the Senate bill throughout the day, with the Senate's top Democrat, Chuck Schumer, saying it had "many, many problems" and would benefit corporate interests at the expense of hospitals, healthcare workers, cities and states.
Speaking of the global spread of the pandemic, the U.S. President said his country is marshaling every resource available to fight the "Chinese virus" and is willing to help and work with other countries including the Democratic People's Republic of Korea (DPRK) and Iran.
The Trump administration has been blaming China for the lack of transparency in the initial handling of the virus and that it has led to the global spread of COVID-19.
On March 16, Trump called the coronavirus a "Chinese virus" for the first time in a tweet and repeated the term days later, which has stirred another war of words between Beijing and Washington.
Beijing has been reacting strongly against such rhetoric, saying it is "smearing China" and Beijing strongly opposes such usage of words.
Speaking to reporters on Sunday, Trump said that he is "upset" with China over a lack of cooperation and information early on in the coronavirus crisis. "They should have told us about this," Trump said. "I'm a little upset with China."
U.S. Secretary of State Mike Pompeo has repeatedly said that Beijing's delay in sharing information about the virus had created risks to people worldwide.
In the past week, Beijing repeatedly refuted the accusations saying Washington attempted to shift the blame to China for its slow response to control the outbreak inside the U.S.
Chinese Foreign Ministry spokesperson Geng Shuang said China imposed strict travel restrictions and quarantine measures in the past two months and such measures had bought time for the world to contain the epidemic and were recognized by the World Health Organization and the international society.
Over a month after Washington pledged 100 million U.S. dollars to coronavirus-hit countries, Geng Shuang told reporters that China "has never received any type of financial aid and assistance from the U.S. government since the outbreak started."
(With input from AFP)
(Cover: U.S. President Donald Trump speaks alongside Vice President Mike Pence during a coronavirus task force briefing at the White House, Washington, DC, U.S., March 22, 2020. /AP)