The leader of Ukraine's ultranationalist Right Sector movement has called on his fighters to continue protests and political actions across Ukraine until those responsible in the deadly shootout in the Ukrainian town of Mukachevo are arrested and the country’s Interior Minister Arsen Avakov steps down.

“Our brothers in arms have been acting in self-defense,” the leader of Ukraine's Right Sector ultranationalist movement Dmytro Yarosh wrote on his page in Facebook.

“We are calling to continue enduring political actions until those who are responsible, in the eyes of the Right Sector, in the deadly shootout [in Mukachevo] (and those are Rada deputy, Mikhail Lanyo and Kiev's special representative for humanitarian issues Viktor Medvedchuk) are arrested and the whole leadership of the law enforcement establishment of the Zakarpatska region and the country’s Interior Minister Arsen Avakov resign,” he added.

© AP Photo / Efrem Lukatsky Activists from the Right Sector party confront police who are blocking a street leading to the Ukrainian Presidential administration building in Kiev, Ukraine, Saturday, July 11, 2015

Saturday's deadly shootout between the Right Sector ultra-nationalist militia and Ukrainian police incited protests in several Ukrainian cities.

The Right Sector activists in Kiev have launched a protest rally in front of the presidential administration building demanding to dismiss Interior Minister of Ukraine Arsen Avakov.

Similar rallies of several dozen people are taking place in the cities of Lviv, Dnepropetrovsk, Kharkiv and Zhytomyr.

Ukraine's Prosecutor General has launched an investigation into the shootout, preliminary qualifying it as a terrorist attack.

Meanwhile, Ukrainian Right Sector militants, blocked in on the outskirts of Mukachevo after deadly clashes with police, are refusing to lay down their arms without their leader’s orders. Civilians in the area have been evacuated, as negotiations so far have failed.

According to reports, Dmytro Yarosh is on his way to Mukachevo.

Authorities said they will do everything necessary to disarm and detain the “organized criminal group”, referring to the Right Sector, that killed one, and injured four civilians. Six police officers were also injured in the standoff on Saturday afternoon.

© AP Photo / A police car is seen on fire at the site of unrest in Mukachevo, Western Ukraine, Saturday, July 11, 2015

“These criminals have killed one and injured four civilians. Six police officers have been wounded, one is in critical condition,” says the statement on the website of the Security Service of Ukraine.

The country’s Security Service also says that three police cars have been destroyed from grenade launchers and machine guns.

Late Saturday, Right Sector issued a statement saying that two of their fighters had been killed and four other wounded.