California Rep. Darrell Issa said Sunday that existing probes into the Obama administration’s FBI and Justice Department “could and will likely lead” to a special investigator, while fellow Republican and South Carolina Sen. Lindsey Graham suggested the time is now for a special counsel to lead such an investigation.

Issa, a member and former chairman of the House Oversight Committee, the chamber’s top investigative panel, made his comments to Fox News’ “Sunday Morning Futures,” after Attorney General Jeff Sessions said last week he would not immediately appoint a new special counsel to investigate Republican concerns involving the FBI and Justice Department.

Sessions instead directed U.S. attorney John W. Huber, a senior federal prosecutor from Utah, to evaluate "certain issues" including whether a special counsel appointment was necessary.

The attorney general’s announcement Thursday came one day after the Justice Department's internal watchdog said it would examine the Republican complaints of FBI misconduct in the early stages of the Russia investigation, which has been led by special counsel Robert Mueller.

That watchdog investigation, led by Inspector General Michael E. Horowitz, was requested by Sessions and congressional Republicans.

They have been urging the inspector general’s office to review whether FBI and Justice Department officials abused their surveillance powers in using information from the controversial anti-Trump dossier, compiled by a former British spy and funded by Democrats, as part of the basis to justify monitoring a former campaign adviser to President Trump.

Issa said Sunday that second-guessing Session’s decision would be “easy.” However, he said getting Huber and Horowitz involved gave such probes credibility and showed they were “looking for truth.”

He also expressed confidence that the inspector general would inform the attorney general about anything that would need a subpoena or be prosecuted.

“I have no doubt about it,” said Issa, who also urged Congress to give the inspector general the “benefit of the doubt” on such matters.

Earlier in the day, GOP Sen. Lindsey Graham, a member of the Senate Armed Services Committee, was more direct about his desire for a special counsel.

“My belief is it should be a special counsel,” he told “Fox News Sunday.” “I want a special counsel with the same determination and resources to look at the abuses of the FISA process, was the Clinton email investigation a sham, were there conflicts of interest in the Justice Department?”

He continued, “I want a special counsel to be appointed with the same resources and the same determination to look at those issues as 'is Mueller looking at the Trump campaign,' and I don’t see that yet.”

The announcement of Horowitz's review came weeks after Republicans on the House Intelligence Committee released a declassified memo that detailed the use of political opposition research to obtain a warrant to monitor Carter Page, the former adviser to Trump's campaign.

The GOP memo described the department's use of information compiled by Steele in obtaining a secret warrant to monitor Page's communications. Steele's anti-Trump research was funded in part by Democrat Hillary Clinton's campaign and the Democratic National Committee.

As the Republicans suggested the FBI may have conspired against Trump, Democrats countered with their own memo that claimed the FBI only “made narrow use” of that research.

Sessions referred the Republican complaints to the inspector general's office, a move that enraged Trump, who denounced it as “disgraceful” and said Sessions should have ordered his own investigation. Sessions insisted he had taken the appropriate step.

The FBI already has been under intense political pressure. Horowitz's office has been examining for more than year the FBI's handling of the Clinton email investigation, an inquiry focused not only on specific decisions made by FBI leadership but also on news media leaks.

That investigation formed the basis of former Deputy Director Andrew McCabe's firing. That inspector general's report has not been released but is expected soon.

Some Republicans praised Horowitz's latest move, including Senate Judiciary Chairman Chuck Grassley, R-Iowa, who has criticized the process for obtaining secret surveillance warrants and had sought an inspector general review.

Democrats have said the investigations have been a waste of money and time.

Under pressure from lawmakers to move more quickly, FBI Director Christopher Wray said last week he had assigned 54 FBI staff to collect documents for separate congressional investigations into the Justice Department initiated by the House Judiciary panel's Republicans. The staff, he said, have been working from 8 a.m. to midnight.

The Associated Press contributed to this report.