MOSCOW—President Dmitry Medvedev said the West was running out of time to secure Russia's consent to set up a U.S.-led missile defense shield in Europe and warned that continuing deadlock would prompt an unspecified Russian response.

Speaking days before a meeting with President Barack Obama and six weeks before leaving office, Mr. Medvedev said on Friday that Russia remained unconvinced by leaders of the North Atlantic Treaty Organization that its planned antiballistic missile shield is meant to deter an attack by countries...