(CNN) Former national security adviser Michael Flynn's offer to testify in return for immunity from prosecution hovered over the investigations Friday into Russia's communications with top aides to President Donald Trump.
Flynn's lawyer, Robert Kelner, said late Thursday that Flynn would testify in exchange for immunity. And Trump himself supported Flynn's request for immunity Friday morning in a tweet, saying, "Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!"
But as of Friday afternoon, it did not appear that investigators had accepted his offer. A Democratic source said that Democrats on the intelligence committee are resistant to the offer.
Rep. Adam Schiff, the top Democrat on the intelligence committee, said Friday it was too early to say whether they would agree to Flynn's request, but put Flynn's offer in greater context.
"We should first acknowledge what a grave and momentous step it is for a former National Security Advisor to the President of the United States to ask for immunity from prosecution," Schiff, who later went to the White House as part of the House's investigation, said in a statement.
A spokesman for House Intelligence Chairman Devin Nunes said that House investigators have spoken with Flynn's lawyer about bringing him in for questioning, but that immunity was never discussed.
The House intelligence committee "had a preliminary conversation with Michael Flynn's lawyer about arranging for Flynn to speak to the committee," Nunes spokesman Jack Langer said. "The discussions did not include immunity or other possible conditions for his appearance."
Spokespersons for the Senate intelligence committee declined to say Friday if the panel would accept Flynn's offer, but a Senate intelligence committee source said it seemed unlikely, although it was too early to say with certainty.
Law enforcement officials told CNN Friday there is no indication the FBI is interested in talking to Flynn again or giving him any kind of immunity.
The FBI has already talked to him and nothing at this point to indicate anything has changed or that they reached out to talk to him again.
Any decision to offer Flynn immunity would come from US Attorneys and Department of Justice, not the FBI, officials explained.
White House Press Secretary Sean Spicer said Friday that Trump believes Flynn should testify before lawmakers and "get the story out" about his ties to Russia.
"He believes that Mike Flynn should go testify," Spicer said during the briefing. "He should go up there and do what he has to do to get the story out."
Spicer said he wasn't going to offer Flynn advice on asking for immunity from the podium, but said Flynn should take every "precaution" in order to get his story out.
In a letter sent Thursday, Trump's top White House lawyer invited the highest-ranking lawmakers on the House and Senate intelligence committees to view classified materials, which it said had been uncovered in the "ordinary course of business."
After reviewing the documents at the White House on Friday, Schiff said in a statement that they were the same documents shown to Nunes by a pair of White House staffers last week.
"While I cannot discuss the content of the documents, if the White House had any concern over these materials, they should have been shared with the full committees in the first place as a part of our ordinary oversight responsibilities," Schiff said. "Nothing I could see today warranted a departure from the normal review procedures, and these materials should now be provided to the full membership of both committees."