Pro-Russian separatists in eastern Ukraine said Thursday they would go ahead with a referendum on secession set for Sunday, defying Russian President Vladimir Putin's call to postpone it and dashing hopes of dialogue with the government in Kiev.

Western capitals had already been skeptical of Mr. Putin's surprise appeal Wednesday, a change of tone that included a claim that Russian troops had pulled back from the border. With the decision by separatists in the Luhansk and Donetsk regions at the heart of the insurgency, the...