WASHINGTON – After a week of fallout from President Donald Trump's decision to fire FBI Director James Comey, Sen. Lindsey Graham on Sunday advised the president to stop talking or tweeting about the ongoing investigations into Russian meddling in the 2016 election.

“The president needs to back off here and let the investigation go forward,” Graham, R-S.C., a member of the Senate Judiciary Committee, said on “Meet The Press.”

He also said he wants to see the next leader of the FBI chosen from within the agency — or someone from “outside the political lane.”

“I think it’s now time to pick somebody that comes from within the ranks or has such a reputation that has no political background at all, who can go into the job on day one,” Graham said.

Republican Senator John Cornyn of Texas, one of Graham’s colleagues in the upper chamber of Congress, was said to be interviewing for the job on Saturday along with several other candidates. Graham called Cornyn a “wonderful man.”

“John Cornyn under normal circumstances would be a superb choice to be FBI director,” Graham said. “But these are not normal circumstances.”

"The president has a chance to clean up the mess that he mostly created," he added. "He really I think did his staff a disservice by changing the explanation. So I would encourage the president to pick somebody we can all rally around, including those who work in the FBI.”

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The Senate Judiciary Committee will get the first chance to examine the president’s pick for the job.

Related: What You Need to Know About Trump, Comey and the Russia Probe

Graham said Sunday he wants Comey to come before the committee so the former FBI director can explain whether he ever felt the president was trying to impede the investigations during their conversations.

“Did the president ever say anything to the director of the FBI that would be construed as trying to impede the investigation?” Graham asked. “The president called me about the firing and he referenced the Comey testimony this week in the Judiciary Committee about how bad it was, so that’s all I know.”

“I think it’s time to call the FBI director before the country at large and explain what happened at that dinner,” he continued, referring to the Jan. 27 dinner at the White House in which Trump reportedly asked Comey for a loyalty pledge. “And if there are any tapes, they have to be turned over. You can’t be cute about tapes.”

Trump had taken to Twitter Friday to rail against the "fake media" and warn Comey that he "better hope that there are no 'tapes' of our conversations before he starts leaking to the press!" When White House Press Secretary Sean Spicer was asked at the daily press briefing later that day if the president had taped Comey, Spicer said, "The president has nothing further to add on that."

Graham called the president's "tapes" tweet "inappropriate."

On Sunday, Graham said multiple times that he does not believe the president is a target of investigations into whether members of the Trump campaign coordinated with the Kremlin, one facet of the various probes being conducted by the FBI and House and Senate intelligence committees.

“I have no evidence that the president colluded with the Russians at all,” Graham said. “Nobody on the campaign that I know of has colluded with the Russians. But we don’t know all of the evidence yet.”

Graham chairs a Senate Judiciary subcommittee that is examining the Russian government's attempts to meddle in U.S. elections, and he requested that Trump provide information about any financial ties he has to Russia. The president's attorneys, a Washington law firm hired to fight the suggestion of business ties to Russia, released a copy of their response on Thursday, but did not provide supporting documents or release copies of Trump's tax returns.

Graham said he had yet to see any evidence of an improper business relationship between Trump and Russians, and that he could not ask for specific documents unless he had a reason. But, Graham said, "the president should turn over his tax returns. He should do that."

"I don't have a reason to subpoena them," he added. "If I get that reason, I'll do it. But he should turn over his tax returns."

Graham also said he stands by his stance that a special prosecutor is not currently needed in the Russia probe because "it is a counterintelligence investigation, not a criminal investigation."

However, as Trump considers a selection to replace Comey as FBI director, some Democrats, like Sen. Mark Warner, D-Va., vice chair of the Senate Intelligence Committee, have said that it could be difficult for the president to get any nominee confirmed in the Senate unless Deputy Attorney General Rod Rosenstein appoints a special prosecutor.

Also on Sunday’s “Meet The Press,” Senate Minority Leader Chuck Schumer, D-N.Y., didn’t deny that Democrats could try to connect the two issues.

“Each Democratic senator’s gonna make up his or her own mind,” he said. “But I think the two are very much related.”

Appointing a special prosecutor and choosing a new FBI director are linked, Schumer said, "because they’re both involved in one of the most serious investigations we’ve seen in a very long time.”