Washington(CNN) A European lawyer pleaded guilty Tuesday to lying to investigators in Robert Mueller's special counsel investigation, after he covered up his discussions with former Trump campaign aide Rick Gates and a business associate based in Ukraine in September 2016, while the Trump campaign operation was in full swing.

The filing is further evidence that Mueller's investigators have ratcheted the pressure on Gates as he negotiates a plea deal and that they continue to look into the work of former Trump campaign chairman Paul Manafort and Gates while they worked for Russian-allied clients and the Trump campaign.

Alex van der Zwaan, a 33-year-old Dutch citizen, said he also lied to investigators about his failure to turn over email communications to the special counsel's office and to his law firm as it cooperated with Mueller on its investigation of Manafort and Gates' foreign lobbying.

Federal Judge Amy Berman Jackson, who also oversees Manafort and Gates' ongoing cases, accepted van der Zwaan's plea during an almost hourlong hearing Tuesday afternoon.

Van der Zwaan faces a maximum of five years in prison and a fine of up to $250,000, though it's more likely he'll serve zero to six months and pay between $500 and $9,500 for his crime, the judge said Tuesday.

He is scheduled for sentencing on April 3.

Until then, the FBI will keep van der Zwaan's passport, and he won't be allowed to travel outside the US. Van der Zwaan must stay in Washington, DC, and Manhattan, where his attorneys are based, until his sentencing, and a judge must review his requests to travel elsewhere within the United States. His sentencing is set at a relatively early date, because his wife is facing a difficult pregnancy in London, his defense attorney told the judge.

His wife, Eva Kahn, the daughter of Russian billionaire German Khan, is due in August.

Van der Zwaan becomes the fourth guilty plea in the Mueller investigation after Trump campaign aide George Papadopoulos and former national security adviser Michael Flynn pleaded guilty to lying to investigators last year, and an online supplier of fake usernames pleaded guilty to identity fraud last week. Mueller has also indicted 13 Russians for their work to influence the 2016 presidential election through online social media.

Unlike other defendants, Van der Zwaan did not enter into an ongoing cooperation agreement with the special counsel's office.

Van der Zwaan's conversation with the special counsel's office in which he allegedly lied happened three days after Manafort and Gates were charged with crimes related to their work for Ukrainian politicians and other business. Both have pleaded not guilty.

In early November, prosecutors questioned van der Zwaan on his work with international law firm Skadden Arps. They were investigating Manafort's, Gates' and other individuals' compliance with the Foreign Agents Registration Act, which governs foreign lobbying and propaganda work for foreign governments in the US, and wanted to know who paid for a Ukrainian report on the trial of a former prime minister and how it was paid for, prosecutors said in court Tuesday.

Van der Zwaan spoke with the special counsel's office a second time in early December to confess to his inaccuracies and what he knew, according to prosecutors' statements in court and a plea agreement released Tuesday.

Ukrainian work

Manafort arranged for the law firm to help the Ukrainian minister of justice in 2012 report on the trial of Yulia Tymoshenko, a former Ukrainian prime minister opposed to Manafort's clients.

At least one public relations firm worked on the rollout of Skadden's report with Gates and Manafort. In total, Manafort and Gates funneled $4 million to facilitate the rollout of the Ukrainian report in the US and Europe, prosecutors said Tuesday.

Van der Zwaan worked with Manafort, Gates and the public relations firm in 2012 to fashion a public spin on the Ukrainian report without his law firm's knowledge.

He had given a public relations firm a copy of the report before its public release, and handed Gates talking points about the report that would help the Ukrainian clients, against the direction of a more senior lawyer at the Skadden law firm, according to court documents and prosecutors' descriptions in court.

Tymoshenko, the subject of the report, is one of the top political rivals of former Ukrainian President Viktor Yanukovych, a Russian sympathizer who used Manafort and Gates as political consultants for more than a decade. After Yanukovych narrowly defeated Tymoshenko in the 2010 presidential election, she was jailed on charges of corruption that were seen by many as being politically motivated.

Skadden produced a report -- intended to be independent -- that said the process was legal. She was freed after Yanukovych's ouster in 2014.

2016 statements

The prosecutors' criminal charge Tuesday explains how van der Zwaan was in touch with Gates and an unnamed colleague of Gates' who was principally based in Ukraine again in September 2016.

They discussed how a criminal complaint in Ukraine could implicate a former Ukrainian official, Skadden and Manafort himself.

The calls were encrypted, and van der Zwaan recorded them and took notes, prosecutors said. At the time, Gates was working with the Trump campaign.

Van der Zwaan had first told prosecutors his last interaction with Gates was an "innocuous text message" in August 2016, leaving out his involvement in the Ukrainian legal discussion.

Van Der Zwaan also deleted and then failed to produce emails he exchanged in Russian in September 2016 with the unnamed person, called "Person A" in court. One of them discussed how the Ukrainian criminal court action was "essentially the tip of the iceberg," prosecutor Andrew Weissmann said in court Tuesday.

When asked by prosecutors why they hadn't seen those emails, van der Zwaan told them he had no idea, and that he hadn't responded to the business associate. But he "knew full well why we didn't get it," Weissmann said Tuesday.

Throughout van der Zwaan's court appearance, the navy-suited defendant leaned far back in his chair and removed his glasses as the judge reviewed his paperwork. At other times, he stood beside his criminal defense attorney William Schwartz to respond to the judge that he understood his plea and his legal rights.

Manafort in Ukraine

Around the time of the conversations van der Zwaan lied about, Manafort was in the spotlight for the work he and Gates did in Ukraine. The New York Times reported that secret documents uncovered in Ukraine listed millions of dollars in illegal payments meant for Manafort, and CNN reported that Manafort's lobbying firm was under scrutiny by the FBI and Justice Department. Days after these reports in mid-August 2016, Manafort resigned from the Trump campaign.

There's no indication from the document that van der Zwaan was in touch with Gates about the political adviser's work in the election, though the charging document is the first evidence that prosecutors have sought -- and potentially even received emails and recorded phone calls related to -- Gates' interactions while he worked for Donald Trump. The separate charges Gates faces in federal court involve activities related to his Ukrainian work with Manafort in years prior to their Trump campaign work.

Skadden Arps said in a statement Tuesday that the firm terminated van der Zwaan's employment last year and is cooperating with authorities. Van der Zwaan was based in London for the firm.

He is the son-in-law of Russian billionaire German Khan, who is one of the most prominent businessmen in Russia. Khan co-founded Alfa Group, a large financial conglomerate, and was recently named in the Treasury Department's list of Russian oligarchs. CNN reported last year that the FBI examined whether there was a computer server connection during the 2016 presidential campaign between Alfa Bank and the Trump Organization, though there isn't any indication that van der Zwaan is connected to that matter.

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 close to plea deal

Gates, meanwhile, has had attorneys working on a plea deal with Mueller's office for more than a month, indicating he's poised to cooperate in the investigation, sources familiar with the case told CNN last week. But no deal has materialized as of Tuesday morning.

He has already spoken to Mueller's team about his case multiple times, CNN first reported last week. His cooperation could be another building block for Mueller in a possible case against Trump or key members of his team.

It would also increase the pressure to cooperate on Manafort, who has pleaded not guilty to Mueller's indictment and is preparing for a trial on alleged financial crimes unrelated to the campaign. Gates pleaded not guilty on October 30 alongside Manafort.

On Friday night, Mueller's office indicated it had unearthed even more evidence of alleged crimes committed by Manafort, related to bank fraud and mortgages on his homes. No charges have been filed related to those accusations as of Tuesday morning.