President Trump earlier this year asked Senator Mitch McConnell, the majority leader, to prioritize a confirmation vote for his nominee to be the chief counsel of the Internal Revenue Service, indicating that it was a higher priority than voting on the nomination of William P. Barr as attorney general, a person familiar with the conversation said.

White House aides insisted for months that the confirmation of the nominee, Michael J. Desmond, a tax lawyer from Santa Barbara, Calif., was a top priority after passage of the tax bill in 2017.

But the request by Mr. Trump, made to Mr. McConnell on Feb. 5, raised questions about whether the president had other motivations. For months, the president has seethed over vows by congressional Democrats that they would move to obtain his tax returns from the I.R.S. And this week, the House Ways and Means Committee chairman, Representative Richard E. Neal, Democrat of Massachusetts, formally asked the I.R.S. for six years of the returns, using an obscure provision in the tax code to do so.

On Thursday, asked if he would direct the I.R.S. not to disclose his tax returns, Mr. Trump said Democrats would have to talk to his lawyers.