"Interior Minister Arsen Avakov and the first deputy head of Ukraine's Security Service (SBU) and head of the SBU's Anti-Terrorist Center Ruslan Baranetsky are on the scene to coordinate the actions of all the involved structural units of law enforcement agencies," the statement says.
Police and SBU agents are working together to free the hostages and ensure public order at the scene.
"In addition, the explosive experts from Volyn region's police department have defused one grenade, which was thrown by the attacker. His identity has been established, this is a 44-year-old resident of Rivne region," the police added.
The city of Lutsk remains closed to ensure the safety of citizens.
"All the forces involved are working in a coordinated manner for the speedy release of the hostages," police said.