Mnuchin said the Small Business Administration planned to do a "full review" of any loans above $2 million before the loans are forgiven. He warned that borrowers have "criminal liability" if they falsely certified that they needed the funds to support operations.

Shake Shack, Ruth's Hospitality Group and other well-known publicly traded companies were among the corporations that received loans before the first wave of funding ran out on April 16. Many have started to return the money amid pressure from the Trump administration and the public.

Mnuchin said it was "outrageous" that the Los Angeles Lakers basketball team was among the enterprises that received a loan before returning it.

"It was inappropriate for most of these companies to take the loans," he said.

The program restarted on Monday with $320 billion in new funding, though banks reported widespread problems with the SBA system they must use to approve loans.

Bank representatives said believed the program was processing about $3 billion in loans per hour. The SBA declined to confirm that figure.

Mnuchin on CNBC did not address growing complaints from bankers about technical glitches with the SBA's system, but he acknowledged in a separate interview on "Fox Business" that the system the agency used for processing the loans had difficulties. He said the SBA worked overnight to address the problems and that believed "we corrected a lot of those issues."

He told CNBC the average loan size, which was about $206,000 before the program's first wave ended, was "coming down" and that the average loan in the backlog was less than $100,000.