"It does not in any way weaken the regulations we put in there for the largest banks or that were there to prevent the kind of crisis we had 10 years ago," said Frank, who co-authored the Dodd-Frank reforms after the financial crisis.
The legislation would raise the level at which banks are considered "systemically important" from $50 billion in assets to $250 billion in assets.
Frank, however, agrees that the $50 billion threshold is too low. He also called $250 billion "too high."
"Lehman Brothers, when it failed, was $750 [billion]. Well, if two or three 250 [billions] were to fail, that could be problematic," Frank said on "Closing Bell."
"I regret that they went above $125 [billion]."
His major objection to the bill has nothing to do with Dodd-Frank.
He said the new bill weakens the reporting requirement on home mortgage disclosures over alleged racial discrimination.
Frank said, "Racial discrimination continues to be a serious problem here and for that reason I wouldn't have voted for the bill."
— CNBC's Jacob Pramuk contributed to this report.