Soldiers and police have been locked in a standoff with a nationalist militia in western Ukraine after a gun and grenade battle that left at least two dead.

Tensions have been rising between the government and the Right Sector militia that has helped it fight pro-Russian separatists in the east of the country.

A Right Sector spokesman, Taras Kuzyak, told Ukrainian media on Sunday that seven infantry fighting vehicles had blocked the entrance to Right Sector’s base near the town of Skole in Lviv region, adding that law enforcement was similarly cutting off access to other Right Sector bases in western Ukraine.

A burning police car in Mukacheve on Saturday. Photograph: STR/EPA

The move came after a gunfight broke out on Saturday, when about 20 Right Sector gunmen arrived at a sports complex controlled by MP Mikhail Lano. They had been trying to stop the traffic of cigarettes and other contraband, a spokesman for the group said.

Near the city of Mukacheve, the site of a fierce gun battle involving Right Sector fighters, private security guards and police on Saturday, Right Sector members were camped in the forest and did not plan to put down their weapons, spokesman Artem Skoropadsky said. It was previously reported that police had surrounded some gunmen in a wooded area and were attempting to negotiate their surrender.

Lano said a Right Sector commander had met him to ask his help in arranging sanatorium stays for men who had fought in eastern Ukraine, during which time an unknown man was shot outside. According to local medical staff, nine people were wounded, including three passersby, in addition to the fatalities.

A video published by journalist-turned-MP Mustafa Nayyem on Sunday shows Right Sector fighters firing Kalashnikov rifles and a heavy machine gun mounted on a pickup truck, apparently in the direction of police who had arrived on the scene. Another piece of footage shows a police car burning.

About 200 people rallied in support of Right Sector outside the presidential administration in Kiev, many of them in military uniforms.

Kiev has allowed nationalist groups including Right Sector to operate despite allegations by groups such as Amnesty International that Right Sector has tortured civilian prisoners.

Despite an official ceasefire that started in February, the conflict in eastern Ukraine continues to simmer. Two Ukrainian soldiers were killed and five wounded in the past 24 hours, a spokesman for Kiev’s “anti-terrorist operation” said on Sunday.

