MOSCOW — Ukrainians voted on Sunday in an early parliamentary election called by President Volodymyr Zelensky, a former comedian who was elected in April, as he seeks to strengthen his position in a country that has been at war with Russian-backed rebels for more than five years.

Mr. Zelensky, 41, has positioned himself as an outsider to Ukraine’s ruling class, which many voters consider hopelessly corrupt. During his presidential campaign, he promised an improvement in living standards and vowed to deliver a peaceful settlement of the conflict with separatists in eastern Ukraine.

Once in office, however, he discovered that his powers were hemmed in by lawmakers from the existing political elites. When he tried to dismiss the foreign minister and the prosecutor general, for instance, Parliament refused to endorse the moves.