Jerome Powell has responded to sharp criticism from the Trump administration about renovations to the Fed’s offices, answering questions about changes to the project as well as reaffirming the central bank’s commitment to “transparency for our decisions and to be accountable to the public.”

For a moment on Wednesday, it looked like President Donald Trump would finally attempt the improbable and fire Federal Reserve Chair Jerome Powell.

The administration has asserted that Mr. Powell has mismanaged the project, resulting in a cost overrun, and it has demanded that he provide answers about the project to the Office of Management and ...