WASHINGTON (Reuters) - Congressional Democrats on Wednesday proposed a bill that would require a U.S. coronavirus supply czar to oversee critical medical supplies, while the top Senate Republican doubled down on demands for business protections.

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Democrats in the Senate and House of Representatives unveiled companion bills requiring the Pentagon to name a civilian officer to oversee the nation’s supply and production of medical supplies and equipment needed to combat the spread of the new coronavirus.

Limited supplies of masks, gloves and testing materials have been blamed for hampering the United States’ response to a pandemic that has now killed more than 58,000 Americans.

The proposals also call for a comprehensive testing plan and a blueprint for scaling up production of an eventual vaccine for the coronavirus, which causes the COVID-19 respiratory disease.

Democrats, frustrated by what they view as Republican President Donald Trump’s unwillingness to seize control of the supply chain for personal protective equipment and testing, want the legislation to be part of Congress’s next coronavirus relief package.

House and Senate Democrats are also pushing for additional funding for state and local governments facing the brunt of the COVID-19 pandemic, with spending estimates of $500 billion for states alone.

House Ways and Means Committee Chairman Richard Neal, in a teleconference with mayors, said Democrats will unveil proposals for helping states and municipalities in coming days and talked about “revenue sharing” as an instrument for delivering the aid.

But Senate Majority Leader Mitch McConnell said the way forward on coronavirus legislation would depend on Democrats’ willingness to agree to protect businesses and others from COVID-related litigation.

“We’re going to insist on this reform, which is not related to money, as a condition for going forward,” McConnell told Fox News Radio.

Democrats dismiss liability protection as a step that could weaken protections for workers.

“Especially now, we have every reason to protect our workers and our patients in all of this. So we would not be inclined to be supporting any immunity from liability,” House Speaker Nancy Pelosi told reporters.

Lawmakers grappled with the prospects of new legislation as U.S. states moved to reopen the economy amid reports of supply and testing shortages that health experts warn could lead to a resurgence of coronavirus infections.

Pelosi also named a slate of Democrats to a new House Select Committee on the Coronavirus Crisis, while promising effective scrutiny of the administration’s handling of trillions of dollars in coronavirus relief funding allocated by Congress.

She said House Republican leader Kevin McCarthy had been invited to name Republican members to the panel. But McCarthy blasted Pelosi’s announcement in a statement that accused Democrats of pursuing an “impeachment 2.0 with a partisan and unnecessary oversight committee.”

The proposed legislation would also require the administration to produce weekly national assessments of equipment supplies, identify available stockpiles and industries capable of filling orders, post state requests for assistance and establish an inspector general to oversee implementation.