Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally MORE (R-Ky.) said Friday that there will be a fourth coronavirus bill and that health care should be a top priority as lawmakers draft the legislation.

McConnell, in an interview with The Associated Press, said that "there will be a next measure."

"[It] 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," he said.

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The comments from the GOP leader, who remains in Washington, D.C., during the Senate's three-week break, are the firmest he has offered yet about the possibility for additional legislation.

Speaker Nancy Pelosi Nancy PelosiPowell warns failure to reach COVID-19 deal could 'scar and damage' economy Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) and House Democrats have held near-daily conference calls with reporters as they've raced to outline their ideas for another coronavirus package that would include infrastructure, free coronavirus treatment and other issues like improved worker protections and expanded family and sick leave.

McConnell acknowledged that he and Pelosi have a "little different point of view" on the timing of the next coronavirus bill, and that he is still "not in favor of rushing" additional legislation.

The GOP leader indicated in a separate tweet that Senate Republicans are focused, for now, on implementing the $2.2 trillion package passed by Congress late last week, which includes direct cash assistance for individuals and hundreds of billions for small businesses and hard-hit industries like airlines.

"Senate Republicans are closely tracking the implementation of our historic CARES Act as the Administration puts it into effect for the American people. We are committed to supporting American workers, families, and small businesses as our nation confronts this historic emergency," he tweeted.

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McConnell's movement toward a fourth bill comes as Pelosi appeared to scale back her ambitions for the next package, saying that things like improvements to drinking water systems and expanded access to broadband may have to wait.

Pelosi told CNBC that the next bill should focus on more funding for direct payments to individuals, unemployment insurance, small-business loans and protective equipment for doctors and other medical professionals.

“Right now, I think that we have a good model. It was bipartisan, it was signed by the president. But it’s not enough,” Pelosi told CNBC host Jim Cramer.

She added that some components of her infrastructure proposal may not make the cut.

“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 this,” Pelosi said.