WASHINGTON — Tony Podesta, a prominent lobbyist and Democratic donor who has come under scrutiny from the escalating special counsel investigation, stepped down on Monday from the firm he co-founded, according to people familiar with the firm.

The firm, the Podesta Group, has lost clients as it has been increasingly drawn into the investigation by the special counsel, Robert S. Mueller III. On Monday, the Podesta Group and another company with which it had worked, Mercury Public Affairs, were referenced — though not by name — in an indictment of two former Trump campaign officials, Paul Manafort and Rick Gates.

No charges have been brought against Mr. Podesta or officials from the Podesta Group or Mercury. But both firms have been subpoenaed for records and testimony about their work on behalf of a client referred to them in 2012 by Mr. Manafort and Mr. Gates, the European Center for a Modern Ukraine, a nonprofit group based in Brussels.

The work for the European Center, which ended in 2014, was cited in the indictment on Monday as part of a “scheme” by Mr. Manafort and Mr. Gates to gain support in Washington for their longtime client, the pro-Russian leader Viktor F. Yanukovych, a former president of Ukraine, while evading disclosure requirements for foreign lobbying.