At least four people were killed by Ukrainian drone strikes across Russia, including Moscow, on Sunday in the biggest attack by Ukraine this year and one of its largest of the war, according to the local authorities and Tass, the Russian state-owned news agency.

Russia’s Ministry of Defense said 556 Ukrainian drones had been intercepted or shot down in more than a dozen regions, according to the local authorities and Tass. President Volodymyr Zelensky of Ukraine said that the attacks on the Moscow region were an “entirely justified” response to Russia’s attacks on Ukrainian cities.

“We are clearly telling the Russians: their state must end its war,” he wrote on social media.

Three people were killed and 12 were injured when drones struck residential buildings in the Moscow suburbs of Khimki and Mytishchi, according to Andrei Vorobyov, the regional governor. India’s Embassy said that one Indian citizen was killed in the Moscow region, and that three more of its citizens were wounded.

Strikes also damaged homes and apartment complexes in four other towns, he said, the latest sign that the war is hitting increasingly close to the heart of power in Russia.

This month, drones struck an upscale residential apartment building a few miles from the Kremlin, as Ukraine intensifies its campaign of long-range attacks deep inside Russia.

Mr. Zelensky had vowed to increase the range and scale of those attacks after a Russian assault on Kyiv killed 24 people last week. On Saturday, he shared a video of what he said were long-range Ukrainian strikes carried out over the past week and warned that “most of the operations are still ongoing.”

Ukraine’s Security Service said it had targeted a plant, a refinery and two oil-pumping stations in the Moscow region. It also said strikes hit military “infrastructure and air-defense” systems at an airfield in Russian-occupied Crimea. Those claims could not be independently confirmed.

Sergei S. Sobyanin, the mayor of Moscow, said drones had struck a checkpoint near the Moscow Oil Refinery on Sunday, injuring construction workers. The refinery’s operations were not disrupted, he said.

Videos published on social media by Astra, a Russian independent media organization, also showed a fire on a runway at Moscow’s Sheremetyevo airport. A spokesman for the airport said that drone debris fell on the airport “at a safe distance from passenger and aircraft service areas.” About 200 flights were canceled, delayed or rerouted.

Concerns about the prospect of Ukrainian deep strikes were seen as the driving force behind the Kremlin’s decision to downgrade its annual military parade on May 9 and to agree a brief truce around the event.

Russia launched 287 attack drones across Ukraine overnight on Sunday. All but eight were shot down, according to Ukraine’s Air Force. At least two people were killed, and around two dozen were wounded.