Mnuchin also clashed with committee chair Maxine Waters.
Rettig said he hadn't been instructed not to comply with the request by anyone acting on the White House's behalf. "We had obviously read in the press that we were expecting this".
The Trump administration will not meet an April 10 deadline issued by the House Ways and Means committee for President Trump's tax returns, Treasury Secretary Steve Mnuchin wrote in a letter to Congress Wednesday.
"We would not ever ask for the White House's permission on this nor did they give us the permission".
Democratic Representative Carolyn Maloney said the communication between Treasury and the White House over the request for Trump's returns was "deeply troubling".
But Democrats have long wanted Trump's tax returns to see what foreign financial dealings he may have, whether he always followed the law, and if he benefited from the 2017 Republican tax overhaul.
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"Congress, as a coequal branch of government, has a duty to conduct oversight of departments and officials", Neal said when he requested the tax returns.
After Mnuchin's request to leave, Waters responded: "Unfortunately, we are all pressed for time", adding that he could "choose to do whatever you want" but she would not close the hearing as other lawmakers had questions for him.
"We did receive the request" for six years of Trump's personal tax returns as well as those for several of the president's business entities, Mnuchin told a House Appropriations subcommittee on Tuesday. "It will be embarrassing if I keep this person waiting for long periods of time", he said. Tax and legal experts have said, however, that an audit should not prevent their public release, a practice presidents have followed for decades.
But many legal experts agree that this law is intentionally open-ended, meaning Congress still needs a legitimate legislative goal to make that request. Neal requested the returns on the basis that he wants to review the procedure for the routine audits of presidents.
The president responded by saying he's under audit - a pretext he has often cited - and "would not be inclined" to release his returns until the audit is completed. "I'm not going to make a specific comment on that, but it would be a good guess".
When Nixon was first audited by the IRS, he was given a clean bill on his returns, but a subsequent audit of the same returns found that he owed almost $500,000 in additional tax on interest.
Neal has adopted a methodical approach to seeking Trump's returns. William Consovoy, one of Trump's lawyers, has advised the IRS and Treasury Department to refuse the request until a legal opinion can be issued. "We are confident that this misguided attempt to politicize the administration of the tax laws will not succeed".