Ukrainian and Russian diplomats, backed by the U.S. and Europe, agreed to take steps to turn down the heat in the escalating standoff with pro-Russian militias, even as President Vladimir Putin showed no sign of backing down.

Talks in Geneva that included U.S. Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov yielded an agreement for separatists to demobilize militias and vacate seized government buildings, and also established a political dialogue that could lead to more autonomy for Ukraine's restive...