George Papadopoulos had pleaded guilty to the charge in 2017 as part of a plea deal in one of the first indictments handed down by the FBI and Mr Mueller's team as part of the investigation into alleged collusion between the campaign team and Russian officials.
Prosecutors said in court filings the former aide severely hindered the early days of the investigation because he lied "at least a dozen" times in a January 2017 interview with the FBI about his contacts with a professor called Joseph Mifsud.
It was at that point "key decisions" were being made by the FBI regarding who to interview, when, and what to ask.
They also said in the filing he lied "to minimise both his own role as a witness and the extent of the campaign's knowledge of his contacts".
As a result, the prosecutors claimed because of Mr Papadopoulos's deliberate deception, the FBI was "substantially hindered [the FBI's] ability to effectively question" Mr Mifsud, who had been in contact with the campaign aide regarding emails which contained "dirt" on then-opponent Hillary Clinton.
The filing by the special counsel's office strongly suggests the FBI had "located" Mr Mifsud while he was in the US during the early part of the investigation, approximately two weeks after Mr Papadopoulos's interview.
The filing stated "the defendant's lies undermined investigators' ability to challenge the Professor or potentially detain or arrest him while he was still in the US," but did not reveal details about the interview which was conducted. Mr Mifsud left the country in February 2017 and has not returned since.
Had Mr Papadopoulos "told the FBI the truth when he was interviewed in January 2017, the FBI could have quickly taken numerous investigative steps to help determine, for example, how and where the professor obtained the information, why the professor provided the information to the defendant, and what the defendant did with the information after receiving it," according to the court filing.
Mr Mueller's team also stated the former campaign aide did not provide "substantial assistance" after his arrest in July 2017 and recommended he also pay a fine of $9,500 (£7,447).
Mr Papadopoulos had said his interactions with Mr Mifsud were "a very strange coincidence" and not related to his campaign work.
However, prosecutors indicated in the court document Mr Papadopoulos and Mr Mifsud began communicating in March 2016, claiming Mr Mifsud "showed interest in the defendant only after learning of his role on the campaign" as an aide.
According to the timeline of events outlined in the court filing, Mr Papadopoulos learned about the "dirt" the Russians had on Ms Clinton the following month, after he began working for the campaign. On the same day as his January 2017 interview with the FBI in Chicago, Mr Papadopoulos applied for a deputy assistant secretary position in Trump's Department of Energy, according to the filing. It took four interviews with the FBI for Mr Papadopoulos to confirm the existence of a foreign mobile he had used, which logged conversations with Mr Mifsud. His lawyers have until 31 August to file their own pre-sentencing memorandum. The former aide is scheduled to be sentenced in the US District Court for the District of Columbia on 7 September.
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In December 2017, former National Security Advisor Michael Flynn also pleaded guilty to lying to the FBI about contacts with former Russian Ambassador to the US Sergey Kislyak. Mr Gates pleaded guilty to several counts of financial fraud, unrelated to the campaign, as well. Mr Manafort is currently on trial for 18 counts of tax evasion and bank fraud. The jury is set to reconvene on 20 August for deliberations.