(CNN) Senate Majority Leader Mitch McConnell said Monday there would likely be more money approved for state and local government relief in the next legislative package Congress passes to address the coronavirus outbreak, a shift in the messaging for the Kentucky Republican.

McConnell last week said he wasn't sure if more money -- which is a key priority for Democrats and many Republicans -- was needed and indicated he was reluctant to provide billions to some state governments he believes have mismanaged their debt.

"There probably will be another state and local funding bill," McConnell said in an interview with Fox News Radio on Monday. "But we need to make sure that we achieve something that will go beyond simply sending out money."

The GOP leader also defended his remarks last week -- that caused an uproar with prominent Democrats including House Speaker Nancy Pelosi and New York Gov. Andrew Cuomo and least a few high-profile Republicans -- that laws should be changed so states can declare bankruptcy to help them shed some of their debt.

"I wasn't saying they had to take bankruptcy. I think it's just an option to be looked at that unfortunately states don't have that option now, cities do. I wasn't necessarily recommending it. But I was pointing out they have their own fiscal problems that predate the coronavirus and I was not interested in borrowing money from future generations to fix age old problems that states have that they created themselves wholly unrelated to this," he said.

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