Gates and former Trump campaign chairman Paul Manafort were indicted in October over their consulting work in Ukraine for the Russian-backed government of one-time President Viktor Yanukovych, who was toppled in a popular uprising in 2014 and fled to exile in Russia.
Special counsel Robert Mueller's prosecutors have filed a new charge against a lawyer they say lied to federal investigators in the Russian Federation probe.
Van der Zwaan is due in court on Tuesday afternoon for a plea hearing.
Van der Zwaan represents the interests of numerous Russian oligarchs. A US judge set his sentencing for April 3.
Until then, the Federal Bureau of Investigation will keep van der Zwaan's passport, and he won't be allowed to travel outside the US. His sentencing is set at a relatively early date, because his wife is facing a hard pregnancy in London, his defense attorney told the judge.
Van Der Zwaan married Eva Khan, German Khan's daughter, at Luton Hoo Hotel, a posh estate outside of London.
The indictment also accuses Mr Van Der Zwaan of deleting or otherwise not producing emails sought by the Special Counsel's office.
Manafort was also one of three top Trump campaign officials who attended a June 2016 Trump Tower meeting with two Russian lobbyists who offered the campaign dirt on the Democratic presidential nominee Hillary Clinton.
Unlike other defendants, Van der Zwaan did not enter into an ongoing cooperation agreement with the special counsel's office.
Both men were charged with 12 counts of conspiracy against the United States, making false statements, money laundering and failing to register as foreign agents for Ukraine.
Van der Zwaan is accused of lying during an interview with prosecutors and Federal Bureau of Investigation agents on November 3, 2017, about the timing of his last communication with Gates and an unidentified person described as "Person A".
The Atlantic also published several emails past year that appeared to show Manafort using his elevated role in the Trump campaign to resolve a financial dispute with the Russian oligarch Oleg Deripaska. The two men were accused of using an offshore account to secretly pay $4 million for the report.
Neither van der Zwaan nor his lawyer immediately responded to calls and emails seeking comment. The firm was helping prepare a report on the trial of Yulia Tymoshenko.
Ms Tymoshenko was jailed the year before for criminally exceeding her powers, charges she said were politically motivated.
The court filing says that van der Zwaan lied to investigators about his interactions with Rick Gates. The following year, with no further work done, Ukraine sent Skadden $1 million.
The calls were encrypted, and van der Zwaan recorded them and took notes, prosecutors said.
Manafort's relationship with Skadden dates to years before his work on the Trump campaign.
He had said that his last communication consisted of an innocuous text message, according to investigators.
Mr Van Der Zwaan is also charged with lying about talks with someone named "Person A". One of them discussed how the Ukrainian criminal court action was "essentially the tip of the iceberg", prosecutor Andrew Weissmann said in court Tuesday.
The charges arose from consultant work for a pro-Russian government in Ukraine. Days after these reports in mid-August 2016, Manafort resigned from the Trump campaign. Skadden's report that year largely supported the charges against her. Manafort then hired the Podesta Group and Mercury Communications to lobby U.S. officials to support Yanukovych, using the report.
In a statement on Tuesday, a spokeswoman for the firm said it had terminated van der Zwaan's employment in 2017 and "has been cooperating with authorities in connection with this matter". Van der Zwaan was based in London for the firm.
Forbes estimates Khan is worth $10-billion.
Van Der Zwaan is the son-in-law of Russian-Ukrainian oligarch German Khan, a co-owner of the Kremlin-linked private bank Alfa Group.
Asked about the charge, White House deputy press secretary Raj Shah told Fox News that the development is unrelated to the President's actions and "only reinforces our point when it comes to the special counsel's investigation. there is no evidence of collusion because none existed".
Gates is finalizing a plea deal with Mueller's office, indicating he's poised to cooperate in the investigation, sources familiar with the case told CNN last week.
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