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.
"You are instructing me to stay here and I am canceling my meeting" with the Bahraini official, Mnuchin said.
"I expect the secretary to honor our invitation to return so that the rest of these members have an opportunity to pursue their questions", she said.
But tax experts say the state returns won't contain the "bombshell" information Trump critics might hope to find. IRS Commissioner Charles Rettig told lawmakers that "we're working on" a response to a request from Ways and Means Committee Chairman Richard Neal.
White House acting Chief of Staff Mick Mulvaney said on Sunday that Trump's tax returns would never be handed over to Democratic lawmakers, in defiance of their efforts to learn more about the former real estate mogul's personal finances.
President Trump said Wednesday he doesn't plan to hand over his tax returns to House Democrats, citing an ongoing audit.
Mnuchin, at the hearing on Tuesday, would not say how he planned to proceed. Fellow Democrat Sen. Mark Warner of Virginia echoed Wyden, urging Rettig to respond to the request for the president's tax returns "without any interference by the Treasury Secretary" or the White House.
Treasury Secretary Steven Mnuchin said in an interview on CNBC television on Wednesday that it was appropriate for his agency to consult with the White House counsel on Neal's request.
"We need to get to the bottom of this", she said.
"It is our intent to follow the law and that is in the process of being reviewed, " Mnuchin told a House Appropriations subcommittee with responsibility for his budget.
Neal, Massachusetts Democrat, set a Wednesday deadline for the IRS to respond, as party lines harden over the request that would give Congress an inside look into Trump's finances and business practices. But the White House is supposed to stay out of the decision, and Rettig said he's had no contact with anyone there.
Also, things got a bit heated at the end of Mnuchin's more than three hours of testimony.
"I am sure there are many prominent Democrats who are relieved that when Kevin Brady [of Texas] was chairman of the committee, he didn't request specific returns", Mnuchin said.
Mnuchin, who'd testified earlier in the day before another House panel, retorted that no other secretary had been treated like him.
Waters, however, told him: "This is a new day and it's a new chair, and I have the gavel at this point". "If you wish to leave, you may". He lost his calm when he was in a hearing with California Representative Maxine Waters.
Mnuchin told Waters, "Please dismiss everybody".
He suggested Waters bang the gavel to adjourn the hearing.
"While I'm under audit, I won't do it", he added, ignoring that the IRS by law is mandated to release the tax returns of an American if requested by the Chairman of the House Way and Means Committee. The IRS is part of Treasury.
Trump has given a range of explanations for why he has not released his tax returns. But Rettig reiterated that there's no rule prohibiting taxpayers under audit from releasing their returns.