But Mr. Strzok was reassigned this summer from Mr. Mueller's investigation to the F.B.I.'s human resources department, where he has been stationed since.
The exact nature of the text messages has not been made public, but defenders of Strzok and Page have reportedly called the allegations "overblown" and said there wasn't any misconduct.
The Justice Department inspector general's office said in a statement Saturday that its investigators are "reviewing allegations involving communications between certain individuals, and will report its findings regarding those allegations promptly upon completion of the review of them".
A spokesperson for Mueller's office said, "Immediately upon learning of the allegations, the special counsel's office removed Peter Strzok from the investigation".More news: Qualcomm alleges that Apple's iPhone infringes on its Palm Pre patents
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Strzok was removed this summer after the inspector general of Justice Department discovered him and another person from Mueller's team exchanging anti-Trump text messages. The people briefed on the case said the transfer followed the discovery of text messages in which Strzok and a colleague reacted to news events, such as presidential debates, in ways that could appear anti-Trump.
The Post has repeatedly sought comment from Strzok and Page, but got no response. Rumors over the cause of Strzok's removal have swirled for months.
President Donald Trump has attacked his own Federal Bureau of Investigation in a series of tweets and said the law enforcement agency's reputation was "in Tatters - worst in History!" The president has also continued his longstanding criticism of the FBI's Clinton email server investigation which Trump initially cited as his reason for firing FBI Director James Comey in May of this year.
Mueller was appointed in May to lead the Justice Department's investigation into whether President Trump or any of his associates colluded with Russian during the 2016 White House race.
Mr Flynn pleaded guilty on Friday to lying to the FBI and agreed to co-operate with Robert Mueller's investigation. Page worked for FBI Deputy Director Andrew McCabe, who conservatives have long complained had a conflict of interest because his wife received campaign funding from Virginia Governor Terry McAuliffe, a close ally of the Clintons for decades.