In a decision sure to disappoint some Republican leaders, Attorney General Jeff Sessions on Thursday rejected requests to name a second special counsel to probe accusations of misconduct at the FBI, saying other investigations should be able to cover the ground.

He announced the decision a day after the Justice Department’s inspector general said he was opening an investigation into the FBI’s use of the anti-Trump Steele dossier to win approval to snoop on a Trump campaign figure in 2016.

Mr. Sessions said the inspector general’s investigation, plus an internal department review by U.S. Attorney John W. Huber, are good enough and there is no need to resort to the extraordinary step of a second special counsel — despite growing calls for such an appointment from Republican leaders on Capitol Hill and from the president’s legal team.

The attorney general said the benefit of this approach is that the inspector general can, in some circumstances, make findings public at the end of his investigation even if no criminal charges are filed — something a special counsel wouldn’t normally do.

He said only two cases have warranted a special counsel since the system was created in 1999, and the FBI investigation isn’t yet one of them.

“Congress created the department’s Office of the Inspector General explicitly for the purpose of, among other things, investigating alleged violations of criminal and civil laws by department employees, including actions taken by former employees after they have left government service,” Mr. Sessions said.

He insisted that Inspector General Michael Horowitz will be able to investigate behavior by former FBI Director James B. Comey, fired Deputy Director Andrew McCabe and others who were involved in approving snooping on Carter Page, a former Trump campaign foreign policy adviser who was subjected to months of wiretapping under the Foreign Intelligence Surveillance Act.

Top Republicans and lawyers working for the president have called on Mr. Sessions to name a special counsel specifically because they believe former officials will be tough to reach. People outside government service cannot be compelled easily to cooperate with inspector generals’ investigations, analysts said.

Two of those Republicans, Reps. Trey Gowdy, South Carolina Republican, and Bob Goodlatte, Virginia Republican, issued a statement expressing disappointment that Mr. Sessions won’t appoint a special counsel. They also voiced support for Mr. Huber.

“While we continue to believe the appointment of a second special counsel is necessary, this is a step in the right direction,” they said. “We expect that U.S. Attorney Huber, given his reputation, will conduct an independent and thorough investigation. Such an investigation is critical to restoring the reputation of both the Bureau and DOJ in the eyes of the American people.”

Mr. Gowdy chairs the House Oversight and Government Reform Committee, and Mr. Goodlatte is chairman of the House Judiciary Committee.

In question is the FBI’s use of an anti-Trump dossier compiled by former British spy Christopher Steele, on orders from the Democratic National Committee and the Clinton campaign. The dossier accused the Trump campaign of colluding with Russia during the 2016 election and included graphic details about frolicking with prostitutes in a Moscow hotel for good measure.

President Trump and his team have denied the claims, and most of the dossier remains unsubstantiated. Mr. Steele has cast doubt on some of his own findings in a court case playing out in London.

The FBI used the Steele dossier to help persuade the FISA court to approve wiretapping Mr. Page — but how instrumental the dossier was, and whether the FBI should have been more suspicious of its information or more forthcoming with the court about the political antecedents, is what Mr. Horowitz will investigate.

Republicans say the FBI shielded key details from the court and that surveillance would have been denied if the bureau had been honest. Democrats counter that the FBI gave the court enough information and argue that the surveillance would have been approved even without the Steele dossier. They point out that the surveillance of Mr. Page didn’t begin until after he had separated from the Trump campaign.

Mr. Steele was dumped as an FBI source after the bureau discovered he was leaking to the press, Republicans say.

Mr. Sessions said he would rely on the recommendation of Mr. Huber on whether a special counsel would be needed.

“I receive regular updates from Mr. Huber and upon the conclusion of his review will receive his recommendations as to whether any matters not currently under investigation should be opened, whether any matters currently under investigation require further resources or whether any matters merit the appointment of a special counsel,” the attorney general said.

An Obama appointee, Mr. Huber resigned when Mr. Trump took office last year, as is the custom for U.S. attorneys upon the change of administrations. Mr. Trump reappointed Mr. Huber shortly after his resignation.

Mr. Huber has spent 13 years as a federal prosecutor and has experience handling violent crime and national security cases, according to the website for the U.S. attorney’s office for the District of Utah.

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