Mueller referred the Craig case to prosecutors in NY a year ago after uncovering possible wrongdoing while he investigated former Trump campaign chairman Paul Manafort's Ukraine lobbying work.
Craig's lawyers rejected the charges.
He served as the White House counsel in the Obama White House from 2009 to 2010.
The charges against Craig, a former Obama White House counsel, arose from the probe by Special Counsel Robert Mueller into Russian interference with the 2016 USA presidential election.
On Wednesday, attorneys for Craig issued a statement in anticipation of charges, arguing that Craig acted only "as an independent expert on the rule of law, not as an advocate" for the Ukrainians. The special counsel interviewed Craig in 2017 about the kind of work he did when he was a senior partner at the law firm Skadden Arps, during which, he supposedly lied.
"The government's stubborn insistence on prosecuting Mr Craig is a misguided abuse of prosecutorial discretion", the attorneys said in a statement to USA media.
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Emails between members of the law firm indicated Craig was concerned about whether the lawyers would need to register under the FARA statute, according to the indictment.
Former Trump campaign chairman Paul Manafort pleaded guilty in September to, among other charges, serving as an unregistered foreign agent and giving false and misleading statements under the FARA statute. In private practice, his clients have included former North Carolina Sen.
In a statement yesterday, Craig denied that he violated the federal Foreign Agents Registration Act, or FARA, which had until recently been rarely used by prosecutors.
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.
Skadden reached a settlement with the Justice Department in January in which it agreed it should have registered as a foreign agent and paid a fine in lieu of prosecution.
Greg Craig was indicted on Thursday for making false claims and withholding information in a federal foreign lobbying inquiry, which coincided in time with Special Counsel Mueller's report. Manafort made the report the centerpiece of a lobbying campaign to improve Yanukovych's reputation in the West, which had suffered as a result of his treatment of Tymoshenko.