Mr Trump's surprising decision last week to fire former FBI Director James Comey - and subsequent reports that the president had allegedly asked Mr Comey to stop the FBI's Russian Federation probe - sent Washington into a frenzy and resulted in several members of Congress calling for special prosecutors to look into the matter.
Chaffetz, the chair of the House Oversight and Government Reform Committee, also said he's prepared to subpoena the memos Comey wrote after his meetings with Trump.
Rosenstein denied media reports from last week that Comey had asked him for additional resources for his investigation before Trump fired him.
Ryan said Wednesday he told congressional Republicans to spend time gathering all the facts on the questions surrounding President Trump, and warned against jumping to conclusions based on news reports.
"I determined that a special counsel is necessary in order for the American people to have full confidence in the outcome", he said.
Shortly after Warner's comments, the committee released a statement from him and chairman Richard Burr, a North Carolina Republican, reiterating their request for Comey to testify and to acting director Andrew McCabe to turn over documents "regarding any communications he may have had with senior White House and Department of Justice officials related to investigations into Russia's efforts".
In closed-door meetings with lawmakers on Thursday and Friday, Rosenstein said he wrote the memo after President Donald Trump told him one day before the May 9 firing that he wanted to dismiss Comey.
In response to the news of Comey's memo, more House Republicans on Tuesday evening called for a combination of White House briefings and public testimony from the former Federal Bureau of Investigation director to assess the scope of the situation.
Analysts are still debating whether Trump actually obstructed justice by asking Comey to drop investigations into Flynn. "That President Trump seems wholly indifferent to this principle, or the potentially devastating consequences of its demise, is the real scandal here". "While the president has repeatedly expressed his view that General Flynn is a decent man who served and protected our country, the president has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving General Flynn", a White House statement said. Comey said he replied that "I agree he is a good guy" but said nothing to Trump about limiting the investigation. During that meeting, Trump shared intelligence about Islamic State terrorists with the Russians.
"We've tried tonight to get Republicans to come out and talk to us, and there are not Republicans willing to go on camera tonight as of yet", host Bret Baier said. After the news broke of the Comey memo, Minority Leader Chuck Schumer, D-N.Y., stood in the chamber and said, "I say to all of my colleagues in the Senate - history is watching".
His dramatic speech was capped off by a warning from the lawmaker overseeing House proceedings: "Members are reminded to refrain from engaging in personalities toward the president, such as accusations that he committed an impeachable offense". He did not deny discussing classified information.