Special counsel Robert S. Mueller III is investigating Russian meddling in the 2016 presidential campaign. (Yuri Gripas/Reuters)

Special counsel Robert S. Mueller III has referred another piece of his investigation to federal prosecutors in New York, asking them to take over an inquiry into whether American lobbyists violated any laws by not registering their work for the Ukraine government, according to people familiar with the matter.

Mueller’s referral — essentially handing an ongoing case over to another prosecutor to determine whether charges should be brought — came months ago, these people said. One said there has not been significant activity in the matter since.

The referral was first reported by CNN on Tuesday. The Washington Post previously reported that Mueller has been winding down some of the investigations he is overseeing, in part by farming out cases to other federal prosecutors. He had referred part of his investigation of President Trump’s former personal lawyer, Michael Cohen, to that same office. That inquiry is ongoing.

Spokesmen for the special counsel’s office and the U.S. attorney’s office in Manhattan declined to comment.

The referral to prosecutors in New York centers on lobbying work done years ago to try to improve the image of the Ukraine government. Federal law requires that Americans who seek to influence the U.S. government on another country’s behalf file paperwork registering themselves as agents of a foreign government.

Mueller’s investigation of those issues led to an indictment against former Trump campaign chairman Paul Manafort. Manafort went on trial Tuesday in Alexandria, Va., on tax and bank fraud charges stemming from the money he received for that work. He faces a later trial in September on charges that he did not register as a lobbyist for Ukraine.

Other Americans, including lobbyists Tony Podesta and Vin Weber, and lawyers at the law firm Skadden, Arps, Slate, Meagher & Flom have come under scrutiny because they worked with Manafort on his pro-Ukraine efforts. It is that part of the investigation that has been referred to New York prosecutors, said people familiar with the matter.

Podesta is the brother of John Podesta, a longtime Democratic adviser who led the presidential campaign of Hillary Clinton. His firm collapsed after he was publicly linked to the Manafort case. The downfall of one of Washington’s most prominent Democratic lobbyists shows how Mueller’s investigation has had consequences for both parties.

Weber works for Mercury Public Affairs, which filed updated paperwork about its lobbying work.

The Podesta Group and Mercury had claimed in lobbying disclosure reports that they represented the European Center for a Modern Ukraine, a Brussels-based nonprofit organization that sought to help Ukraine improve its image in the West from 2012 to 2014. Prosecutors allege that behind the scenes, however, the lobbying work was being directed by Manafort and Trump campaign official Rick Gates, and that their real client was the government of Ukraine.

The two firms have said they are cooperating with the special counsel’s investigation.

On Tuesday, Michael McKeon, a partner at Mercury, said: “We welcome any inquiry, as we always have, since we acted appropriately at every step of the process, including hiring the best lawyer in Washington we could and following his advice.”

A lawyer for Tony Podesta declined to comment. A representative for the Skadden law firm did not immediately respond to a request for comment.