Pasechnik said the attack occurred while the bus was travelling through the region but did not immediately provide details about the type of weapon used or the circumstances surrounding the incident.
According to information released by the Russian-installed authorities, the passenger bus was travelling from Lysychansk to Kadivka when it came under attack.
The identities of those killed have not yet been released, and it was not immediately clear whether there were any other passengers injured in the incident.
Luhansk, located in eastern Ukraine, has been one of the major areas affected by the conflict between Russia and Ukraine. Parts of the region have remained under Russian control, while fighting and attacks have continued in several areas.
Russia and Ukraine have repeatedly accused each other of carrying out attacks on civilian areas and infrastructure in territories affected by the war. Independent details surrounding the latest attack on the passenger bus were not immediately available.
The attack comes as the war in Ukraine continues to take a heavy toll on civilians, with both sides reporting regular missile, drone and artillery attacks in areas close to the front lines and beyond.
Authorities in the Russian-controlled part of Luhansk said they were continuing to assess the situation and gather further information about the attack.
