Craig, 74, was indicted by a grand jury in Washington on Thursday following an investigation that grew out of US special counsel Robert Mueller's inquiry into Russian interference in the 2016 presidential election. He has denied any wrongdoing, the US media reported.
Craig faces up to five years in prison for each of the two counts. He is the first prominent Democrat to face criminal prosecution as a result of Mueller's probe, which led to the conviction of President Donald Trump's former campaign chairman Paul Manafort for a series of financial crimes.
Craig was charged with giving false information during an October 19, 2017, interview with the special counsel's office which regulates work in the US by lobbyists, lawyers and other representatives of foreigners under the Foreign Agents Registration Act (FARA), according to CNBC.
He is accused of lying to the Justice Department about his work on a 2012 report aimed at justifying the prosecution of a political enemy of Ukraine's pro-Kremlin President Viktor Yanukovych, who was later ousted. Craig's lawyers declined to comment.
He was also charged with concealing details of his work from the same officials.
Craig's attorneys said that the charges were unfair and that prosecutors had chosen to omit evidence that was favourable to him. "Craig had no interest in misleading the FARA unit because he had not done anything that required his registration," they said.
"That is what this trial will be all about."
Prosecutors said on Thursday that, if convicted, Craig could also be fined up to $100,000 and $250,000 for the respective charges.
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