The far-right Right Sector group is also demanding the resignation of police officials in the city of Mukacheve, where the deaths occurred on Saturday.
Dozens of Right Sector supporters took to the streets in central Kiev, calling for an end to the “persecution” of the group’s members.
Right Sector, which played a prominent role in the Kiev street protests in 2014 that toppled former Moscow-backed president Viktor Yanukovich, said two members had been killed and four wounded. Six police officers are also reported to have been wounded.
In the video above, released by the Ukrainian Interior Ministry, the men in military uniform are said to be members of Right Sector. Some elements of the video are mute.
The group’s spokesman Artem Skoropadsky said Interior Minister Arsen Avakov bore political responsibility for what happened and should resign.
Referring to the shootout, he said Right Sector members were trying to “stop flows of contraband”, adding that the group had paramilitary volunteers all over Ukraine. The group’s website said these volunteers were on combat alert.
Ukrainian officials accused Right Sector of attacking property belonging to a local politician and firing at police officers with guns and grenade launchers.
The ousting of Yanukovich set off a confrontation with Russia and sparked the worst east-west crisis since the end of the cold war.
Analysts said the latest violence was a direct challenge to President Petro Poroshenko and his government and could threaten to open up a new front in Kiev’s battle to bring order to Ukraine.
When a new government was formed in Ukraine this year, several politicians linked to the far right were given posts. Among them was Right Sector leader Dmytro Yarosh, who was appointed an adviser to the army chief of staff.