Mr Yarosh, leader of the Pravdy Sektor (Right Sector) party, confirmed he would be running for Ukraine's top political job and launched an attack on Ukraine's current political leadership.
He said there was a "loss of public confidence" in Ukraine's interim government, led by interim Prime Minister Arseniy Yatsenyuk.
Mr Yarosh, who is staunchly anti-Moscow, is wanted by Russia on terrorism charges after allegedly inciting a Chechen warlord to attack Putin's country.
In an interview with Channel 4 News Europe Editor Matt Frei last week, Mr Yarosh said he was not a neo-fascist.
His paramilitary movement, which wears black combat gear and ski masks, was integral in the Maidan protests that led to the departure of ousted president Viktor Yanukovych.
Mr Yarosh was given the post of deputy secretary of the Security and Defence Council, Ukraine's top security body, in the interim government. He is likely to run against former international boxing champion Vitali Klitschko, former Foreign Minister Petro Poroshenko and former Prime Minister Yulia Tymoshenko in the presidential elections.
Russia has claimed that Ukraine's leadership has been taken over by nationalist, far-right elements, which they have accused of being "anti-Semitic" and "neo-fascist".
However, Volodymyr Fesenko, a political analyst at Penta think-tank, says it is highly unlikely Mr Yarosh would be elected.
"Yarosh has no chance of winning," he said. "The most he could get is about 3 per cent of votes."
In Crimea, the Russian controlled region in the south of Ukraine, military tensions escalated over the weekend.
Overnight, Russian troops seized a military defence post in Sevastopol and Ukraine's border service said Russian troops had also seized a border guard outpost in the east of the peninsula, kicking the Ukrainian officers and their families out of their apartments in the middle of the night.
Ukraine's border guards also said that an observation plane travelling along Crimea’s border on Saturday was fired upon. Nobody was said to have been hurt.
Self-defence military units swore allegiance to Crimea's new authorities in a ceremony attended by self-designated Crimea leader Sergei Aksyonov. Aksyonov said troops stationed in Crimea and not loyal to the region's new authorities must disarm.
Hundreds of Russian troops in a convoy of fifty vehicles were also reported to have travelled through Crimea’s capital, Simferopol, on Saturday, heading into a base.
And tensions were further exacerbated when a monitoring team from the Organisation for Security and Cooperation in Europe (OSCE) had to turn back from Crimea after warning shots were fired.
It is the third time that the team has tried to enter Crimea, but the first time that warning shots have been fired.
The OSCE monitors were requested by Kiev, but have not been given permission by Crimea's pro-Russian separatist regional authorities.
Polish Foreign Minister Radoslaw Sikorski said on Saturday Poland had evacuated its consulate in Sevastopol due to "continuing disturbances by Russian forces".
Moscow has maintained that the troops in Crimea are not under its command. The troops do not have insignia on their uniforms – but it is widely accepted that the vehicles, weapons and uniforms on show come from the Russian military.