The former FBI director has been appointed as a special counsel to investigate allegations of collusion between Mr Trump’s associates and Russia, following evidence of Kremlin meddling in the 2016 presidential election.
At the weekend it emerged Mr Mueller’s investigators had obtained tens of thousands of emails exchanged by 13 members of Mr Trump’s transition team – leading almost immediately to claims by a Trump lawyer they had done so unlawfully.
Kory Langhofer told members of Congress some of the communications released by the General Services Administration (GSA) were “privileged” in a number of ways, and asked them to “act immediately to protect future presidential transitions from having their private records misappropriated by government agencies”.
But Mr Mueller’s spokesman insisted the proper protocol had been followed, while two members of Mr Obama’s transition team dismissed Mr Langhofer’s allegations as “whining”.
Norm Eisen, deputy general counsel for the 2008 transition and later Mr Obama’s ethics czar, wrote on Twitter: “I warned everyone: there is NO expectation of privacy in your transition emails. The clue: emails are ‘firstname.lastname@example.org.’ The whining letter from the Trump Transition tacitly admits this.
“Executive privilege does not apply until you are the executive; these documents are from the transition, before Trump became the executive; QED no executive privilege. Grasping at straws here.”
Chris Lu, who led the 2008 transition, added: “There is no expectation of privacy in transition emails: 1) they have a .gov address; 2) they were created with govt-supplied equipment; and 3) they sat on govt servers. This is just whining from Trump team”.
The President has also criticised Mr Mueller’s gathering of the emails, saying it was “not looking good” and insisted again there was “no collusion”. He denied rumours he was planning to fire the veteran prosecutor from his role as special counsel.
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Mr Langhofer said some of the emails were “protected by the attorney-client privilege, the deliberative process privilege, and the presidential communications privilege”, and asserted that releasing the messages constituted “unlawful conduct that undermines the Presidential Transition Act”.
In a seven-page letter he further claimed that Richard Beckler, then the GSA’s general counsel, had promised to forward any requests for disclosure to Trump For America’s lawyers. Mr Beckler died in September, aged 77.
However, a colleague who was also present for that conversation said no such promise was made.
In using electronic devices provided by the GSA, Mr Trump’s team was told that material “would not be held back” from law enforcement, Lenny Loewentritt told Buzzfeed News.
Among the officials who used transition email accounts was Michael Flynn, who later became National Security Adviser but was fired and, earlier this month, pleaded guilty to lying to the FBI. His lawyer, Robert Kelner, did not comment.
When the news broke on Saturday, White House spokeswoman Sarah Huckabee Sanders said the administration would “continue to cooperate fully with the special counsel and expects this process to wrap up soon”.
Mr Mueller’s spokesman, Peter Carr, said his office had followed the law when requesting documents.
“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,” he said.
Elijah Cummings, the ranking Democrat on the House oversight and government reform committee, said: “Our committee has direct jurisdiction over the Presidential Transition Act, and it simply does not support withholding transition team emails from criminal investigators.
“The President’s lawyers have said they want to fully comply with special counsel Mueller’s investigation, so it is odd that they now suggest they would have withheld key documents from federal investigators.”
Eric Swalwell, a Democratic congressman who sits on the House judiciary committee, categorised Mr Langhofer’s claims as “baloney” and an attempt to turn opinion against Mr Mueller.
“‘Private documents’ on a US Government, public email system? What are they afraid was found? Baloney. This is another attempt to discredit Mueller as his #TrumpRussia probe tightens,” he wrote on Twitter.
Additional reporting by agencies