A consultant to Sen. John McCain hired a public-relations firm last year to burnish the U.S. image of a Ukrainian political party backed by Russian leader Vladimir Putin, according to documents filed with the Justice Department.

The lobbying firm of Davis Manafort Inc. arranged for the public-relations firm's work through an affiliate last spring, at the same time Davis Manafort was being paid by the Republican presidential candidate's campaign. The firm is co-owned by lobbyist Rick Davis, manager of Sen. McCain's presidential...