Peter Strzok, a senior counterintelligence investigator, also suggested that the Republican Party "needs to pull their head out of their ass," USA Today reported.
Strzok was removed from Mueller's staff earlier this year after Justice Department investigators began reviewing whether investigators had shown bias against Trump.
Strzok's reference to Trump as an "idiot" came in an email exchange with another agent, Lisa Page, in August, 2015.
"He's an idiot like Trump. Figure they cancel each other out," Strzok replied.
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In a March 2016 message, Page exclaimed: "God trump is a loathsome human....omg he's an idiot."
"He's awful," Strzok replied.
Special counsel Robert Mueller removed Strzok from his Russia election meddling probe this summer after becoming aware of the emails.
Page by that time had already ended her assignment in Mueller's office, according to Politico, one of several US news organizations that obtained copies of the email.
The messages turned up as part of a Justice Department inspector general investigation into potential political influence on investigative decisions during the campaign.
Mueller is looking into whether Trump campaign aides or associates colluded with Russian efforts to sway the 2016 election in the Republican real estate mogul's favor.
Former Trump national security advisor Michael Flynn and George Papadopoulos, a campaign foreign policy advisor who maintained Russian contacts, have pleaded guilty to lying to the FBI.
Former Trump campaign Paul Manafort and his partner Rick Gates have pleaded not guilty to money-laundering charges related to their previous political work in Ukraine.