Mr. Sentsov denies carrying out or planning violent acts. Russia says he is a Russian citizen because he lived in Crimea, which is now part of Russia. Mr. Sentsov says he is Ukrainian.

Mr. Sentsov, 41, is being held in a prison for hardened criminals, nicknamed the Polar Bear, in the Arctic town of Labytnangi.

The campaign to free Mr. Sentsov has picked up with the opening of the World Cup. The filmmakers Pedro Almodóvar and Wim Wenders are among those who have rallied to Mr. Sentsov’s cause.

On Wednesday, the day before the tournament began, the European Parliament passed a resolution demanding Mr. Sentsov’s release and calling him one of 70 Ukrainian “political prisoners” being held in Russia.

It is unclear whether the attention has helped the chances of Mr. Sentsov’s release.

President Vladimir V. Putin of Russia has played down the possibility of a swap that includes Mr. Sentsov. Earlier this month, he said Mr. Sentsov should not be traded for a Russian journalist held in Kiev, Ukraine’s capital, because the cases were not comparable.

On both sides, the prisoners’ fates have been tied up with the on-again-off-again diplomacy over ending the war, and exchanging detainees. Some type of swap had appeared imminent before the soccer tournament began; it was discussed last weekend in a telephone call between Mr. Putin and President Petro O. Poroshenko of Ukraine, the Kremlin said, though no prisoners have been freed.