WASHINGTON — President Trump’s lead lawyer, Rudolph W. Giuliani, said Wednesday that lawyers for several people facing scrutiny from the Justice Department in the investigations into the Trump campaign and presidency had contacted him to see whether the president would pardon their clients.

Mr. Giuliani declined to identify the lawyers who broached the subject with him or their clients. He made his statement in response to questions about Mr. Trump’s former lawyer and fixer, Michael D. Cohen, who has told federal prosecutors in Manhattan about pardon discussions last year that involved Mr. Giuliani and a lawyer who was expressing interest in representing Mr. Cohen, according to people briefed on the matter.

The disclosure from Mr. Giuliani — and the new details about pardon discussions involving Mr. Cohen — highlighted again the continued questions about Mr. Trump’s pardon power and how he might use it as the special counsel, Robert S. Mueller III; other federal prosecutors; and Democrats in Congress investigate his political and business careers.

The discussions acknowledged by Mr. Giuliani demonstrate that, at the very least, some of those under investigation, or their lawyers, believed that it was worthwhile to ask about whether a pardon was on the table.