Senator Mitch McConnell, Republican of Kentucky and the majority leader, alarmed and angered state officials on Wednesday when he said he wanted to approach the next round of pandemic legislation more deliberately. He said he was opposed to shipping money to state governments if they were going to apply it to fiscal problems unrelated to the pandemic, such as shoring up underfunded pension plans for public workers.

Rather than looking for handouts, Mr. McConnell said, states should consider filing for bankruptcy. His aides threw fuel on the fire in a news release that said the Senate leader was opposed to “blue state bailouts,” suggesting it was Democratic-leaning states that were seeking the money to take care of problems caused by fiscal mismanagement.

Mr. Trump gave ambivalent signals about further aid to state governments at his White House briefing on Thursday, suggesting that he might be open to offering it but also echoing Mr. McConnell’s language, which had outraged Democratic governors like Andrew M. Cuomo of New York. “It is interesting that the states that are in trouble do happen to be blue,” Mr. Trump said.

Mr. Cuomo accused Mr. McConnell of hyperpartisanship, calling the “blue state bailout” label “vicious.”

“How ugly a thought,” he said. “Think of what he is saying. People died — 15,000 people died in New York, but they were predominantly Democrats, so why should we help them?”

The National Governors Association, a bipartisan group of governors, wrote federal officials this week pleading for $500 billion to help them make up for lost tax revenues during what they called “the most dramatic contraction of the U.S. economy since World War II.”

The group’s chairman, Gov. Larry Hogan of Maryland, a Republican, told Politico on Thursday that he thought Mr. McConnell would come to regret his remarks. “The last thing we need in the middle of an economic crisis,” he said, “is to have the states all filing bankruptcy all across America and not able to provide services to people who desperately need them.”