President Volodymyr Zelensky of Ukraine said President Vladimir V. Putin of Russia would escalate his bombing campaign as the American midterm elections approach, in an interview with the Spanish newspaper El País published on Friday.

Mr. Zelensky spoke at a school in Kyiv that a Russian drone had struck on Thursday morning, part of an intensifying air assault on the capital that he said was meant to drive its residents out. “They want Ukrainians — especially those in the capital — to leave. In fact, that’s what they were aiming for when the full-scale invasion began,” he said. In the same wave of attacks, a drone hit one of the bridges over the Dnipro River as a subway train was crossing it.

Classes had already begun when the school was hit. The students were moved to a bunker under protocol and no one was hurt. The newspaper’s special correspondent, Luis de Vega, described air raid sirens sounding again moments before the president arrived, smoke rising nearby and the thud of air defenses, while a member of the security detail scanned the sky with binoculars. The visit continued. A 14-year-old student named Valentín, who said he was glad he had overslept, pointed to the damaged upper floors: “That floor is the library, the one below is the computer lab.”

“Remember that in 2022, that was their goal: to get people to leave the capital to prove that, if you don’t have the capital, you don’t have a country,” Mr. Zelensky said. “But our country is more than just the capital, and the capital remains strong.”

“These are not military targets, nor are they on the front lines,” he said of the recent strikes. “They are attacking to paralyze the city and prevent people from going to school or work.” He listed Russia’s objectives as logistics, including food and hospital supplies, agriculture, and schools, all aimed, he said, at “simply destroying people’s ability to live.” The goal, he added, was chaos: “They’re trying to plunge Ukraine into chaos, and of course it’s understandable that people are becoming demoralized.”

He predicted the tempo would rise with the approach of the Nov. 3 vote in the United States, where the House and one-third of the Senate are up for re-election in a test of support for President Trump. “Putin’s tactic is to escalate the conflict as much as possible, and he will do so,” Mr. Zelensky said. “And as the U.S. midterm elections approach, he will do so more and more.”

Mr. Putin, he said, “is not afraid of Europeans, nor is he affected by sanctions, and, of course, it directs its messages primarily at the United States.” He recalled warning Jared Kushner and Steve Witkoff, Mr. Trump’s negotiators, when they visited Kyiv on Sept. 6 that “they would see — especially after the election — massive attacks that would directly affect the civilian population.” Despite his past clashes with Mr. Trump, he said he remained confident the American president could play a role in ending the invasion.

Mr. Zelensky named Russia’s enablers: “China, India, and other countries are really helpful in allowing him to circumvent sanctions” and “they also provide military equipment,” he said, while “the Iranians” contribute “military expertise with drones.” He described Tehran as the source of much of the military power Moscow has built up for this war.

Ukraine, he said, has built a large domestic industry producing defensive drones and other systems, allowing it to stand up to one of the world’s leading military powers. But he conceded a gap: the country lacks enough weaponry to stop ballistic missiles, which have hit their targets more than 90 percent of the time this year, according to Ukrainian statistics.

He promised to keep seeking foreign funding for weapons production, arguing the war now bears little resemblance to the one that began on Feb. 24, 2022. Whatever Kyiv raises, he added, “it won’t be enough.”