"I don't think that you can have any more than one president at a time," Christie told CNN's Jake Tapper on "State of the Union."
"And, you know, General Flynn has said up to this point that he had not said anything like that to the Russian ambassador. I think now he's saying that he doesn't remember whether he did or not," Christie said, pointing to a discrepancy in what Flynn told Vice President Mike Pence previously and what he said after reports of those conversations emerged last week.
Flynn cannot rule out that he spoke to a Russian official about sanctions, an aide close to the national security adviser said Friday.
Flynn, the aide said, has "no recollection of discussing sanctions," but added that the national security adviser "couldn't be certain that the topic never came up."
"So, that's a conversation he is going to need to have with the President and the vice president to clear that up, so that the White House can make sure that they are completely accurate about what went on," Christie said.
Christie did not call for the White House to take any specific action to reduce Flynn's role.
"That would be up to the vice president and the President," Christie said. "And so I'm sure there will be conversations between the vice president, the President and Gen. Flynn to make sure that everybody gets the accurate story on this matter and that it's cleared up. And I think that's the obligation of Gen. Flynn."
White House senior policy adviser Stephen Miller deflected questions about whether Flynn should be fired, calling it a "sensitive matter."
"It's not for me to answer hypotheticals. It wouldn't be responsible. It's a sensitive matter," he told NBC's Chuck Todd on "Meet the Press," adding that the White House "did not give me anything to say" on the issue.
"That's the question that I think you should ask the president, the question you should ask Reince (Priebus), the chief of staff," Miller said.