Rudolph W. Giuliani, the former mayor of New York, denied a report on Monday that he was being considered as a replacement for Mr. Sessions and expressed support for him, telling CNN he “made the right choice” to recuse himself from the Russia inquiry.

Mr. Sessions has been forceful in pressing the Trump administration’s agenda in its first six months, enacting hard-line policies on immigration and criminal charging and sentencing, and dismantling some significant legacies of the Obama administration.

Addressing federal prosecutors on Friday in Philadelphia, Mr. Sessions signaled that he wanted to charge ahead in enacting policy priorities “under Trump’s direction.”

Key constituencies, including many members of law enforcement, said they had no desire to see the Justice Department’s leadership upended. “From our standpoint, the attorney general is doing a fine job in furtherance of the president’s agenda,” said James Pasco, the senior adviser to the president of the Fraternal Order of Police.

He said that Mr. Trump had “made exactly the right choice for attorney general.”

Mr. Sessions has underscored his subordinacy to Mr. Trump in recent days, standing in contrast to the emphasis he has placed for years on the independence of Justice Department officials.

As a longtime member of the Senate Judiciary Committee during his years as a Republican senator from Alabama, Mr. Sessions repeatedly asked Justice Department nominees to pledge their independence from the president.

In 2015, in questioning Sally Q. Yates before her confirmation as deputy attorney general, Mr. Sessions made clear that he believed the Justice Department should push back if the president ever issued an “improper” directive. “You have to watch out because people will be asking you to do things,” Mr. Sessions said, “and you need to say no.”