Nicole Gaudiano, and Kevin Johnson

USA TODAY

WASHINGTON — Deputy Attorney General Rod Rosenstein has indicated that he is not yet inclined to appoint a special prosecutor to take over the FBI's inquiry into possible collusion between the Trump campaign and Russian officials, a person familiar with the matter said Friday.

The ultimate decision on whether to seek an outside counsel, which Democrats have demanded following President Trump's abrupt dismissal of FBI director James Comey on Tuesday, falls to Rosenstein because Attorney General Jeff Sessions has recused himself from any involvement in the Russia probe.

The latest details on Rosenstein's position on the matter, which was first reported by CNN, comes as the Justice Department leader agreed to brief the full Senate on his role in President Trump's firing of Comey.

Rosenstein, who along with Sessions recommended Comey's dismissal, informed Senate Democratic leader Chuck Schumer's office on Friday that he would meet with senators next week, according to Matt House, Schumer's spokesman. The time and date are still being worked out, he said.

Rosenstein is certain to face grilling from Democrats, who have ramped up their calls a special prosecutor to takeover the Russia investigation. Sen. Dick Durbin of Illinois, the Senate's No. 2 Democrat, pushed the issue further on Friday, saying Rosenstein should appoint a special prosecutor or resign.

Contrary to his administration's early assertions, Trump told NBC’s Lester Holt on Thursday he would have fired Comey regardless of Rosenstein and Sessions' recommendation. He added that he was thinking of "this Russia thing" when he made the decision, calling it a "made-up story."

In a morning tweetstorm, he appeared to threaten Comey if he leaked information to the media, saying he'd better hope there are no "tapes" of their conversations.

Durbin cast Trump's statement on NBC as an admission that he fired Comey because of the Russia investigation, which he said is "dangerously close to obstruction of justice." He said Trump's tweet could be another violation of law.

"This morning, the President tweeted a thinly-veiled threat to Mr. Comey, which could be construed as threatening a witness in this investigation, which is another violation of federal law," Durbin said in a statement. "To preserve his reputation as a credible prosecutor, Deputy Attorney General Rod Rosenstein must appoint an independent special prosecutor to pursue possible criminal charges, or he must resign."

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In a memo to Sessions justifying Comey's dismissal, Rosenstein cited Comey’s controversial handling of the investigation into former secretary of State Hillary Clinton’s use of a private email server. But there has been wide skepticism among Democrats and some Republicans about the president's motives.

Because of Rosenstein's role, Schumer has argued that a non-political appointee of the Justice Department should be responsible for tapping a special prosecutor rather than Rosenstein. He called on Senate Majority Leader Mitch McConnell, R-Ky., to invite not only Rosenstein but Sessions to brief all senators in separate and possibly classified meetings.

McConnell has said that opening a new probe into the Trump campaign's alleged Russian connections would impede the work of the Senate Intelligence Committee's investigation.

Comey had been invited to testify before the committee on Tuesday, but the panel's top-ranking Democrat said on MSNBC on Friday that won't happen. Virginia Sen. Mark Warner said he hopes Comey will appear before the committee in the "not too distant future."

"I have enormous respect for Jim Comey and I believe that at the appropriate time and place he's going to tell his side of the story and my hope is that that place at least will be in front of our committee," Warner said.