WASHINGTON—The Russian lawyer whom Donald Trump Jr., Jared Kushner and Paul Manafort met last year with the hopes of receiving damaging information about Hillary Clinton says she talked with the office of Russia’s top prosecutor while waging a campaign against a U.S. sanctions law and the hedge-fund manager who backed it.

Lawyer Natalia Veselnitskaya said she wasn’t working for Russian authorities, but she said in an interview with The Wall Street Journal that she was meeting with Russian authorities regularly and shared information...