Militants from far right armed group ‘Right Sector’ clashed with police in western Ukraine on Saturday. Kiev called the incident an "act of terror," while the group said its forces would stand against the authorities across the country.

Four civilians and three police officers were injured in a shoot-out in the city of Mukachevo in the Zakarpattia region of Ukraine's south-west, according to the country's Interior Minister Arsen Avakov. The fighters used grenade-launchers, the minister added in his Facebook post.

One of the four injured civilians later died in a hospital, Ukraine's Interior Ministry representative Artem Shevchenko said on Ukrainian TV.

The ultranationalist group said on its website two of their fighters were killed and four injured in the incident. Authorities said three fighters were killed.

The regional public prosecution office said six officers, three civilians and five fighters were injured. Authorities labeled the incident an act of terror.

Clashes involving firearms started on Saturday, when fighters reportedly opened fire at a local sports center after failing to split spheres of interest with a local MP. Police arrived at the scene, and heavy arms including grenade-launchers and machine guns were used in the shoot-out, local media reported. A fire started at a nearby petrol station, with several cars having been reportedly damaged as well.

There have been reports that nearby Slovakia has tightened security at its border with Ukraine due to the incident.

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While authorities said the armed group was rounded up and ordered to surrender, the fighters claimed they had escaped and demanded that the government arrest police officers who fired at them. Some of Ukraine's other far-right groups, including the "Organization of Ukraine's nationalists" battalion, announced their support for the Right Sector fighters.

Right Sector leader Dmitry Yarosh also called for the arrests of policemen involved in the incident, and said he was headed for Kiev to stop the bloodshed, RIA Novosti reported. The extremists have called on all their supporters to gather in Kiev on Saturday evening by the president's administration building. The group was on combat alert, RIA cited its press-service as stating.

Nationalist forces from other regions were moving towards the town, Ukrainian media reported, while law enforcement backing was being sent to the area. All roads to Mukachevo are reportedly closed, with fighting said to be continuing in the area. Anti-terror units of Ukraine's Security Service were in charge of the special operation, Interior Ministry official Anton Gerashchenko said, adding that talks would continue with the fighters to put down arms.

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President Poroshenko ordered law enforcement services to disarm and detain those in charge of the Saturday shooting, the president's spokesperson Svyatoslav Tsegolko announced on Facebook. The country must stand against any "display of banditism, wherever it occurs," the statement said.

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The Ukrainian Right Sector political and military group of radical nationalist organizations has been involved in numerous clashes with police and officials since January 2014. The ultranationalist party, which is officially banned in Russia, has also taken part in fighting rebels in eastern Ukraine. The extremists have rejected the Minsk ceasefire agreement, having called on President Petro Poroshenko to renew the military offensive in the eastern part of the country.