After an editorial in a Ukrainian newspaper raised questions about that low figure, Manafort and Craig scrambled to respond, prosecutors say.
"I did not participate in a scheme to mislead the government or hide material facts", he said. A spokesman for the US attorney's office declined to comment.
Craig also coordinated public relations work to boost the government's image.
The federal investigation began as an offshoot of the Mueller probe that was later handed off to Manhattan federal prosecutors. Craig's former firm, Skadden, Arps, Slate, Meagher & Flom, was hit with a $4.6 billion fine for working with Paul Manafort in 2012 on behalf of Ukraine. Craig left Skadden in April 2018.
Fox News is now reporting that a former White House counsel for then-President Barack Obama was indicted Thursday for "making misleading" statements to Robert Mueller's team regarding his relationship with Ukrainian officials.
Craig has privately represented prominent political figures, including former North Carolina Senator John Edwards, and is regarded within the legal world as a powerhouse. He held jobs in the Bill Clinton presidency as well, and even helped Clinton mount a defense in the face of impeachment.
The report was meant to be an objective review of the Ukrainian government's prosecution of Yulia Tymoshenko, the country's former prime minister who was convicted in 2011 on corruption charges and sentenced to seven years in prison.
As part of his probe, Mueller brought FARA charges against Manafort for his work on behalf of Yanukovych and his pro-Russia Party of Regions. Craig - while on the payroll of the Yanukovych government - found that the Yanukovych government's prosecution of its opponent met worldwide standards, in a report that was widely dismissed as a whitewash.
After the FARA unit then concluded that the firm needed to register as an agent of Ukraine, Craig and other Skadden attorneys met with members of the FARA unit in October 2013, and Craig "made false and misleading statements", particularly that "his media contacts were exclusively reactive and for the objective of correcting misinformation". It admitted it was paid $4.6 million for the report, and not the $12,000 the Ukrainian government said at the time.
"Craig did not want to register as an agent for the government of Ukraine, however, least in part because he believed doing so could prevent him or others at the law firm from taking positions in the federal government in the future", court documents said. The false statements charge is the same one that Special Counsel Robert Mueller brought against numerous defendants during the Russian Federation probe.
"The only time we responded, was to correct misinformation", Craig wrote. Like Manafort, who also worked with Yanukovych, Craig did not register as a foreign agent for this work.
In the statement Wednesday, Craig's lawyers denied that he lied to the government or his firm.
"I never discussed the finding of our report to any USA officials. I think we don't have to with this assignment, yes?" he wrote in a February 2012 email.
Craig's lawyers, William Taylor and William Murphy, called the indictment "unfair and misleading". Mr Craig was not named in the settlement. "That is what this trial will be all about", they said in a statement.
"The goal of FARA is to prevent covert influence by foreign principals", the indictment read.
Under US law, all lobbyists for foreign governments must register with the department.
In the last few years, the Justice Department has brought several high-profile prosecutions involving FARA.
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