WASHINGTON (AP) — Senate Majority Leader Mitch McConnell said Friday that health care must be at the "top of the list" in the next coronavirus  rescue package.

In an interview with The Associated Press, the Republican leader said Congress should focus on correcting any shortcomings in the just-passed  $2.2 trillion aid bill and rely on health care experts for solutions to "wipe out" the virus.

"There will be a next measure," McConnell said about what would be the fourth coronavirus aid bill from Congress.

The Kentucky Republican said the next package "should be more a targeted response to what we got wrong and what we didn't do enough for — and at the top of the list there would have to be the health care part of it."

The GOP leader's remarks, alongside comments Friday from House Speaker Nancy Pelosi, signal a potential thaw after days of political sniping and promise a new opportunity for Congress to work in a bipartisan way to fight the pandemic gripping the nation.

Pelosi said Friday that the next coronavirus aid bill should build on the bipartisan relief bills  that Congress has passed so far rather than include broader Democratic agenda items, such as infrastructure and rural broadband access.

That's a noteworthy pivot for the California Democrat, who earlier has pressed goals such as a large public works measure and the restoration of a deduction for state and local tax payments.

"While I'm very much in favor of doing some things we need to do to meet the needs — clean water, more broadband, the rest of that — that may have to be for a bill beyond that right now," she said during an appearance on CNBC.

She told reporters at the Capitol that she spoke with McConnell Friday.

McConnell acknowledged that he and Pelosi have "a little different point of view" about the timing of the next package, as the congressional leaders have jousted in separate television and media appearances all week.

McConnell maintained he is "not in favor of rushing" into the next phase until they take stock of how the just-passed bill is working and what corrections are needed.

But the focus on health care has potential broad appeal as the crisis afflicts communities of all sizes and in all corners of the country, with sick patients seeking treatment at increasingly overrun hospitals and emergency rooms.

"We've got to wipe this out and we've got to wipe it out in warp speed," McConnell said. "And so I would put that at the top of the list of places we need to look and see what could we have done better in the previous bill, the $2.2 trillion."

He added: "We can't sustain economically this happening again. We've got to solve the health part of it, which means not only treatment but vaccines."

The leaders' remarks came as fresh evidence arrived of the gravity of the economic crisis caused by the outbreak. The latest batch of unemployment figures showed that a record, almost decade-long streak of U.S. job growth ended last month.

At the same time, the crisis is hitting closer to home. A 400-bed field hospital  is being set up at the University of Kentucky's Lexington campus, officials said Friday. A day earlier the state's governor announced plans to set up a 2,000-bed field hospital at the state fairgrounds in Louisville.

"We need a fourth bipartisan bill," Pelosi said.

In a hallway conversation with a small group of reporters, Pelosi said a $350 billion program to help keep small businesses afloat should be extended, as well as unemployment insurance for the jobless and a direct payment to most Americans.

"Let's do the same bill we just did, make some changes to make it current and correct some of the things that we'd like to see," Pelosi said. She also would like more generous aid for state and local governments facing budget crises because of plummeting sales and income tax revenues and higher costs for coronavirus response and safety net programs.

Pelosi's shift followed criticism by Republicans that she was seeking to take advantage of the crisis to press ambitious Democratic agenda items that couldn't pass on their own. McConnell made it clear that Republicans wouldn't agree to such add-ons.

GOP leaders across the board have lambasted Pelosi for citing the crisis as a reason to restore the federal tax deduction for state and local taxes. Putting the deduction back in place would have chiefly helped higher income earners in high-tax, Democratic-run states such as California, New York and New Jersey. The idea was widely panned and was seen as unrealistic, given opposition from Republicans.