The Trump administration would support another round of tax rebate checks and help for restaurants, hotels and airlines as part of the next coronavirus aid package, Treasury Secretary Steven Mnuchin said Thursday.

Outlining potential elements of a new aid package, which Congress plans to negotiate later this month, Mnuchin said he is also working on a “technical fix” to any extension of expanded unemployment benefits so that workers don’t earn more in benefits than they would on the job.

Those benefits, which were enacted in March and will expire at the end of this month, currently provide an extra $600 a week to jobless workers, on top of their regular state-issued benefits.

Mnuchin, who has served as the administration’s point man on aid talks, told CNBC’s “Squawk Box” that he had conferred Wednesday with Senate Majority Leader Mitch McConnell and White House Chief of Staff Mark Meadows about a new package. McConnell has said he hopes to unveil a Republican proposal by the time the Senate reconvenes on July 20.

McConnell said Monday that a new round a tax rebate checks should be limited to lower-income people. The previous round from March provided checks to single filers of up to $1,200, with the amount awarded phased out completely for those earning more than about $99,000 a year.

“I think the people who have been hit the hardest are people who make $40,000 a year or less,” McConnell said in Kentucky. “Many of them work in the hospitality industry.”

Mnuchin declined to say whether he would endorse such an income threshold. “We do support another round of economic impact payments,” he said. “The level and criteria we’ll be discussing with the Senate.”

[Senate GOP aid package may tailor payments to low-income households]

House Democrats passed a nearly $3.5 trillion aid package in May, but McConnell and Trump administration officials have suggested they are aiming for a measure that costs no more than about $1 trillion.

House Speaker Nancy Pelosi flatly rejected that cost target Thursday. “What doesn’t measure up is, ‘Oh, it can only be a trillion dollars,’” she said at a news conference. She said $1 trillion would be needed just for aid to state and local governments, which have seen their revenue plummet from an economic shutdown due to the pandemic.

Pelosi also rejected McConnell’s income target threshold for new tax rebate checks. “I don’t know where the $40,000 came from,” she said. “I think families making over $40,000 probably need assistance.”

She said another $1 trillion should be provided for extension of unemployment insurance and a new round of direct payments to households. Pelosi added that “something like that, but probably not as much” would be necessary for health care needs such as testing, contact tracing and treatment.

Mnuchin said any extension of the Paycheck Protection Program, which offers forgivable loans to small businesses, must be “much more targeted” than the current program. While the program has been credited with providing fast relief to about 5 million businesses, it has also come under fire for giving loans to high-priced lobbying shops and law firms, among other wealthy recipients.

And the Treasury chief again made clear White House concerns about robust aid to state governments, though he stopped short of ruling out any such aid. “We are not going to bail out states that were mismanaged before the coronavirus,” he said.

Republicans have also made liability protections for school districts and businesses a prerequisite for additional federal aid to states and localities. Pelosi didn’t rule out a compromise on that front, but said any such indemnification would have to be limited.

“We think there’s a path to talk about protecting businesses and workers and customers who come in,” Pelosi said. “But, don’t say, ‘You all have to go back to work, even if it isn’t safe. And by the way, we’re removing all responsibility from the employer.’ I mean, that’s — no.”

Lindsey McPherson, Jessica Wehrman and Jennifer Shutt contributed to this report.