(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 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.

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 Friday's White House 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.

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