WASHINGTON — Mick Mulvaney, the White House budget director, spent the weekend managing the shutdown of the federal government. On Tuesday, he turned his attention back to his secondary job running the Consumer Financial Protection Bureau, a government agency he would probably shut down if he could.

In a 1,118 word mission statement that was sent to the bureau’s staff on Tuesday, Mr. Mulvaney, the acting director, outlined a vision for an agency that enforces financial regulations and consumer protections with “humility and prudence” and that will no longer “push the envelope” when it comes to jurisdiction and scope. Mr. Mulvaney insisted that he would not shutter the bureau, if only because doing so would be against the law.

“When I arrived at C.F.P.B., I told folks that despite what they might have heard, I had no intention of shutting down the Bureau,” Mr. Mulvaney wrote. “Indeed, the law doesn’t allow that, and as members of the Executive Branch we are charged with faithfully executing the laws.”

The consumer bureau, which was created by the 2010 Dodd-Frank law, has been an ongoing target of Republican lawmakers, who complain that its mandate is too broad, that it has too much power and that its director is unaccountable. The agency is loathed by Republicans because its authority is intended to be independent of the White House and Congress.