The building is said to have been some kind of school building with dormitories. One of the fatalities was a child, according to the authorities' account. Around ten people have also been injured, and a rescue operation is still underway in the rubble, reports Ukraine's state emergency service.
Images published in Ukrainian state media show how a multi-story segment of a brick building has completely collapsed on the ground.
Ukraine's President Volodymyr Zelenskyj drew attention to the deadly attack on Hluchiv on Tuesday morning and described it as an example of Russia not wanting peace with Ukraine:
"Every day, we appeal to the international community to show enough determination and strength to enable Ukraine to stop these attacks on our people. Every new attack from Russia confirms Putin's true intention: He wants the war to continue."
Hluchiv is located near the border with Russia in the Sumy region. Earlier in the morning, the regional military administration reported that Russia had launched a total of 27 attacks on various communities on the Ukrainian side of the border, using both drones and artillery.
On Sunday, eleven people were killed when a Russian cluster bomb hit a residential area in the city of Sumy, with many more people also injured. On Monday, ten people were killed in a massive Russian missile attack on Odessa in southwestern Ukraine, where the projectiles caused fires in residential buildings on the ground.