Mueller's latest move comes just a day after former USA attorney Harry Litman said he thought the president's former campaign manager will be sent to jail by Friday.
"Manafort and Kilimnik repeatedly contacted Persons D1 and D2 in an effort to secure materially false testimony", prosecutors alleged in court papers.
Manafort's lawyers, in a court filing on Friday, asked the judge to reject Mueller's request, saying "the text messages cited by the special counsel do not establish any witness tampering".
They said Kilimnik may have reported to Russian intelligence officers in Moscow or Kiev or both on his work at the International Republican Institute office in Moscow where he was employed for a decade to 2005 and later on his work for Manafort in Ukraine.
US Special Counsel Robert Mueller filed new criminal charges on Friday against President Donald Trump's former campaign manager Paul Manafort while also indicting a longtime associate of Manafort's with alleged ties to Russian intelligence.
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That meeting, which will be hosted by Canadian Prime Minister Justin Trudeau , will be Trump's first visit to Canada as president. Mnuchin said he had informed Trump of his discussions but that trade was only one of many issues on a full agenda.
Kilimnik, according to court papers, wrote a message to the other executive two days later saying: "Basically P wants to give him a quick summary that he says to everybody (which is true) that our friends never lobbied in the U.S., and the objective of the program was European Union".
The additional charges could add to pressure on Manafort to cut a deal and cooperate with Mueller's probe, legal experts said.
Prosecutors have previously said Kilimnik has ties to Russian intelligence, which he denies.
"From a scant record, the Special Counsel conjures a sinister plot to "corruptly persuade" two of Mr. Manafort's former business associates to perjure themselves at the upcoming trial in September", their filing said.
The government has not charged Manafort with the crime of witness-tampering or obstruction of justice.
Kilimnik has denied to journalists that he has any connection to Russian intelligence.
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Manafort is awaiting trial in federal court in Washington and Alexandria, Virginia.
Before Kilimnik was identified by name in charges on Friday, he had made multiple appearances in Mueller's filings as an unidentified intermediary for Manafort. The individuals shared communications with prosecutors, the government said.
Mueller said in a statement earlier this week the two men had tried to influence witnesses' accounts of Manafort's attempts to lobby on behalf of pro-Russian political parties in Ukraine.
The new charges will factor heavily into whether U.S. District Judge Amy Berman Jackson allows Manafort to remain on house arrest. "Closer scrutiny of this 'evidence" reveals that the Special Counsel's allegations are without merit because Mr. Manafort's limited communications can not be fairly read, either factually or legally, to reflect an intent to corruptly influence a trial witness". He has been charged with money laundering, tax and bank fraud, and conspiracy in two federal cases as part of Mueller's ongoing probe.
Asked on Friday if he would pardon Manafort, Trump refused to answer.
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Kilimnik worked for Manafort's longtime business partner, Rick Gates, when they served as political consultants in Ukraine. Kilimnik later took on more responsibilities, serving as Manafort's liaison to Oleg Deripaska, a Russian billionaire who paid Manafort to advise him on investments.