Johnson told CNN that he thinks there needs to be a change to the law to say that those transition emails, administered by the General Services Administration, are not the property of the federal government.
"We're going to have to potentially update the laws ... to make it very clear that even though this is housed at GSA, this is not government property," said the Wisconsin Republican, who planned to write a letter to GSA to get more clarity on what happened. "I think those are some legitimate issues they raised."
Johnson added that "we need to look at the transition law and maybe clarify those issues. ... I think they are definitely private emails, so we need to clarify that."
Attorneys for the Trump presidential transition wrote to the House and Senate oversight panels to argue that the emails, which were on a government domain, were its property and should not have been turned over without its approval.
Johnson said the question about whether Mueller had obtained the emails legally needs to be fought in court, echoing his House counterpart, GOP Rep. Trey Gowdy of South Carolina.
Gowdy told CNN he's not interested in weighing in on the Trump transition team's complaint that Mueller "unlawfully" obtained its emails.
But Gowdy, a former federal prosecutor, said he's generally inclined to side with prosecutors trying to obtain information. And he argued that it's a court matter, unless Congress wants to pass a law to deal with presidential transitions.
"My bias is what you'd expect of a prosecutor who has spent most of his life trying to get information," Gowdy said. "Ultimately, there's only really one opinion that matters, and that's the trial judge who hears the motion."
Peter Carr, spokesman for Mueller, said in response to the accusations from President Donald Trump's lawyers, "When we have obtained emails in the course of our ongoing criminal investigation, we have secured either the account owner's consent or appropriate criminal process."