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Senate Minority Leader Chuck Schumer and President Trump’s newly installed Chief of Staff Mark Meadows discussed appointing a czar to oversee production and distribution of medical supplies and equipment to help combat the novel coronavirus, Fox News has learned.

Schumer, D-N.Y., and Meadows spoke over the phone Sunday night about the federal response to COVID-19, specifically, with respect to the administration’s efforts in New York, which has become the epicenter of the virus in the U.S.

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A source familiar with the phone call told Fox News that Schumer urged Meadows to have the president fully invoke the Defense Production Act, which allows the president to direct manufacturers to make certain equipment necessary for the U.S. to deal with a crisis, whether that be a war or a pandemic, in order to “promote the national defense.”

Schumer also urged Meadows to convince the president to appoint one person in his administration as a czar to oversee production and distribution of critical supplies, as many Democrats and some in the media have criticized the Trump administration’s efforts as disorganized.

Schumer has been calling for a senior military official to be tasked with these responsibilities for most of the last week and has even spoken directly with the president and Vice President Pence about the topic. His call with Meadows late Sunday, though, was the first time he floated specific names of potential officials to take on the role.

Schumer proposed former vice chairman of the Joint Chiefs of Staff General Paul Selva; former vice chairman of Joint Chiefs of Staff and former NORTHCOM Commander Admiral Sandy Winnefeld; and Vice Adm. Mark Harnitchek, who served as director of the Defense Logistics Agency.

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Last week, the president mocked Schumer's proposals.

“Somebody please explain to Cryin’ Chuck Schumer that we do have a military man in charge of distributing goods, a very talented Admiral, in fact,” Trump said Thursday.

The president, in late February, appointed Rear Adm. John Polowcyzk, a senior Navy officer, to be in charge of leading FEMA’s coronavirus supply chain.

Polowcyzk leads the Supply Chain Task Force, which is made up of both FEMA and officials from the Department of Health and Human Services. The task force’s primary effort is the sourcing of personal protective equipment (PPE), ventilators and other critical resources requested by states and localities. The task force is working to close the gap between the private sector and the federal government.

The task force also is focused on accelerating manufacturing, expanding the industry and helping manufacturers to re-tool assembly lines to produce new products needed in the fight against the virus, and allocating the resources to ensure the right quantities get to the right place.

It is unclear whether the president will consider Schumer’s proposal, and what a "czar" would do differently than Polowczyk and his task force.

Schumer's negotiations with the White House come amid criticism that the federal government has not acted quickly enough to provide states and hospitals with necessary supplies and PPE for medical professionals.

Trump has recruited large companies, like Ford Motor Company and General Motors, to manufacture tens of thousands of ventilators that hospitals across the country need for patients suffering from severe complications of COVID-19 -- as well as working with Walmart and other supply companies for PPE for those on the front lines.

As of Monday morning, the U.S. reported more than 337,900 positive cases of COVID-19 and more than 9,600 deaths.

Fox News' John Roberts and The Associated Press contributed to this report.