Ukraine and Russia on Saturday appeared to be seeking to avoid a broader confrontation in the wake of Kiev's claim it destroyed most of a Russian military convoy that entered its territory, as the European Union intensified its efforts to bring the two countries to the negotiating table.

Col. Andriy Lysenko, the Ukrainian government's security spokesman, said Saturday that Ukrainian artillery had destroyed most of a Russian column of military vehicles that entered the country earlier in the week. But he described the episode...