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On Friday, Mykhailo Podolyak, a senior adviser to Mr. Zelensky, said in a post on the Telegram messaging app that if Ukraine’s western neighbors would shoot down Russian missiles from their territory, it would “allow Ukraine to concentrate its scarce antimissile systems in the east and south of the country,” which are under near daily attack.

Amid concerns that the conflict could spill over, the Pentagon said on Saturday that it was sending an antimissile battery and battalions of the Patriot ground-based air defense system to the Middle East.

Included in the package drawn from Pentagon stockpiles are several Stryker armored personnel carriers, mine-clearing equipment and munitions for Patriot antimissile systems and National Advanced Surface-to-Air Missile Systems, or NASAMS, the officials said.

The overnight attack early Thursday left very little time for residents to take shelter, with antimissile defenses colliding with missiles just six minutes after the air alarm sounded, the Kyiv military administration said.

The Kinzhal, which is an air-launched version of an Iskander ballistic missile, is believed to meet the definition of a hypersonic weapon — namely that it can fly and maneuver at speeds equal to or greater than five times the speed of sound, a feature meant to defeat antimissile defenses.