Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) on Monday said that Congress will "probably" pass additional funding for state and local governments in forthcoming coronavirus relief bills.

McConnell, during an interview with Fox News Radio, opened the door to the new funding and appeared to soften his remarks about allowing states to declare bankruptcy amid the pandemic.

"There probably will be another state and local funding bill but we need to make sure that we achieve something that will go beyond simply sending out money," McConnell said.

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McConnell added that negotiating further aid for state and local governments would be "challenging" and reiterated that Republicans don't want funding to go toward overstretched state pension programs.

"We do want to help them with expenses that are directly related to the coronavirus outbreak but we're not interested in helping them fix age-old problems that they haven't had the courage to fix in the past," McConnell said.

McConnell's comments come after the GOP leader sparked backlash, including among members of his own party, when he told radio host Hugh Hewitt that he was supportive of allowing states to declare bankruptcy. A GOP leadership aide added subsequently that McConnell was responding to a hypothetical raised by Hewitt and not indicating future GOP strategy.

"I would certainly be in favor of allowing states to use the bankruptcy route. It saves some cities. And there’s no good reason for it not to be available. My guess is their first choice would be for the federal government to borrow money from future generations to send it down to them now so they don’t have to do that. That’s not something I’m going to be in favor of," McConnell said at the time.

Asked about the comments on Monday, McConnell said that he was not trying to indicate that states should have to declare bankruptcy.

"It was just an option to be looked at," McConnell said, adding that he wasn't "necessarily recommending it."

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Congress's $2.2 trillion package passed last month included $150 billion for state and local governments. But the $484 billion bill passed last week did not include any additional funding, with GOP senators warning that trying to include it would likely have prevented the bill from passing the Senate without a formal roll call vote.

Democrats view getting more help for state and local governments as a top priority for the fifth coronavirus bill.

But McConnell on Monday laid out his own "redline" for the upcoming bill, saying he wants to limit legal liabilities for hospitals and businesses as they plan to reopen.

“Trial lawyers are sharpening their pencils to come after healthcare providers and businesses, arguing that somehow the decision they made with regard to reopening adversely affected the health of someone else," McConnell said.

“So before we start sending additional money down to states and localities, I want to make sure that we protect the people we've already sent assistance to, who are going to be set up for an avalanche of lawsuits if we don't act," he added.

—Updated at 8:32 p.m.