Medical supplies and equipment-including masks, respirators and gowns-are on their way to the three states, Trump said, and should be there within days, per NBC.
"We are taking more tests in NY than any place else", said Cuomo.
Opposition Democrats want the emergency stimulus bill, which is worth nearly $1.4 trillion (£1.2 trillion), to include more money for state and local governments and hospitals, while Mr Trump's Republicans are pushing for quick action to reassure financial markets.
Gov. Andrew Cuomo has repeatedly said that New York State's original capacity of 53,000 hospital beds and 3,100 intensive-care beds - which are fitted with vitally-important ventilators - will not be enough to satisfy the demand of hospitalizations that will be caused by the virus, the Advance/SiLive.com reported.
At the daily briefing, President Trump said he had approved NY and Washington's requests to declare a major disaster amid the COVID-19 pandemic, and was about to approve California's request too.
Trump asked. "They're very, very sick, and we can use it on those people and maybe make them better and in some cases maybe save their lives".
Italy to use army to enforce coronavirus lockdown in worst-hit region
Italy's death toll from the coronavirus outbreak eclipsed China's on Thursday as the scourge extended its march around the world. In the United States, Treasury Secretary Steven Mnuchin urged Congress to pass a $1-trillion emergency stimulus package.
Cuomo on Sunday called for the nationalization of the effort to create and acquire medical supplies needed to manage the coronavirus outbreak at healthcare facilities.
Trump said that governors in each state would be "in command locally" of the National Guard, underscoring the importance of a specific response on a state-by-state level.
Senate Majority Leader Mitch McConnell has urged senators to "signal to the public that we're ready to get this job done".
Meanwhile, a hospital in Washington state - once the centre of the U.S. outbreak - said it could run out of ventilators by April. It was later surpassed by NY state, which has now become the epicentre of the outbreak in the country.
Talks between Democrats and the White House are continuing.