Mnuchin made the announcement after the Internal Revenue Service, which he oversees, missed the deadline to release the returns -- set by House Ways and Means Chairman Richard Neal -- passed at 5 p.m. Tuesday.
"Although federal law establishes no deadline for a response to your request, we expect to provide the committee with a final decision by May 6, after receiving the Justice Department's legal conclusions," Mnuchin wrote in a letter to Neal.
Mnuchin added the release of the tax returns could "threaten the privacy of all tax payers" unless carefully restrained by law.
"History demonstrates that private tax return information is susceptible to abuse for partisan purposes -- regardless of which party is in power," Mnuchin wrote.
Neal directly requested the release of the records from IRS Commissioner Charles Retting, who also sent him a letter Tuesday, saying the agency had not yet mad a final determination on how to respond.
We "are awaiting further guidance and direction on legal issues external to the internal review laws before doing so," Retting wrote.
In a statement Tuesday, Neal said he plans to consult with his counsel about the "next steps" to obtaining the records, potentially setting up a lengthy legal battle for their release.
Democrats have criticized Mnuchin for taking the lead on the decision, which they state is Retting's to make, but Retting has stated that Mnuchin is his boss.
Tuesday's deadline was the second set by Neal after Mnuchin told him the Treasury Department needed more time to examine the issue and consult with the Justice Department two weeks ago.