Rep. Trey Gowdy, R-S.C., said calls for a special prosecutor to investigate possible connections between President Donald Trump's campaign and Russia were coming "too soon."

"There is no special prosecutor statute. There is no independent counsel statute," Gowdy told Fox News' "America's Newsroom" co-anchor Bill Hemmer on Tuesday.

"There's a regulation that allows for the appointment of special counsel if the Department of Justice has a conflict and if all 92 U.S. attorneys have a conflict. Until that evidentiary burden has been satisfied, I don't know why Republicans or Democrats are talking about special counsel," he added.

"It's too early. Special counsel only applies to a criminal investigation," he added, noting that Congress does not investigate crimes, the FBI does.

Gowdy's colleague and fellow Republican Rep. Darrell Issa of California, a senior member of the House Judiciary Committee, called for a special prosecutor while on "Real Time with Bill Maher" Friday. He also said that U.S. Attorney General Jeff Sessions should step back from the process.

"You cannot have somebody, a friend of mine Jeff Sessions, who was on the campaign and who is an appointee. You're going to need to use the special prosecutor's statute and office to take — not just to recuse," he said.

"You can't just give it to your deputy. That's another political appointee."

Former House Speaker Newt Gingrich called for an "independent" investigator to look into reports of contact between Trump campaign officials and members of the Russian government, during an interview on Fox News Tuesday, according to NBC News.

When prompted if a special prosecutor should be used, Gingrich said Trump should "take a lesson from the past" by appointing a "very smart, independent person" to investigate.

"Maybe somebody like Michael Mukasey, former attorney general [for George W. Bush] — put them in charge of the whole project, and say, you know, there are questions here, the country has questions, the media has questions, even members of Congress (have0 questions," Gingrich said.