"We're peaceful men," said 46-year-old Mikhailo cheerfully, as he poured petrol into a row of glass bottles to create molotov cocktails. "We're just making them. Other people will throw them."

The intensity of the violence in Kiev, which began late on Sunday night and culminated on Wednesday morning with three deaths, has taken many people both inside the country and abroad by surprise. While during the two-month course of the protests there were two incidents when riot police attacked protesters brutally, there has not been a large-scale response from the protesters. Suddenly, this week, the police found themselves under a hail of molotov cocktails, their buses torched and several hundred people unwilling to give their ground and ready to engage them in violent clashes.

After two months of protest with little result, the mood is very different to that back in December. Then, when riot police attempted to remove the barricades surrounding Independence Square in a night-time charge, protesters handed back helmets and shields to officers who got stranded in the crush and sent them on their way. After the surge, groups of officers could stand unmolested at the side of the square. Now, feelings have intensified. When a molotov cocktail lobbed at police lines broke on the torso of an officer and turned him into a human candle, whoops of joy went up from the crowd.

But while some of the violent inclination appears to stem from the frustration of those who saw their peaceful stance ignored, there also appear to be more shadowy forces at work. Pravy Sektor, a murky grouping of nationalist and far-right groups, has said it is co-ordinating the violence, and the coalition represents very different ideals from the initial protest goal of closer links with the European Union.

Andriy Tarasenko, one of Pravy Sektor's co-ordinators, agreed to meet the Guardian in a cafe in central Kiev. Wearing a rollneck jumper and with a quiet voice, he seemed a far cry from the warriors on the street, but his message was clear.

"For us, Europe is not an issue, in fact joining with Europe would be the death of Ukraine. Europe means the death of the nation state and the death of Christianity. We want a Ukraine for Ukrainians, run by Ukrainians, and not serving the interests of others."

Tarasenko said the goal of the group was a "national revolution" that would result in a "national democracy" with none of the trappings of the "totalitarian liberalism" that the EU represents for him.

He also has little time for the trio of opposition politicians who have been the de facto protest leaders, including the former heavyweight boxer Vitali Klitschko. "The only negotiations with [President Viktor] Yanukovych should be about how he gives up power. If any of these leaders were capable of seizing power, they would have done it already."

The number of people taking goggle-eyed selfies in front of the burning barricades and looking on in disbelief suggests that those who feel they are peaceful protesters who have been driven to this by the uncompromising nature of the authorities are still in the majority.

Hardcore Ukrainian nationalism is not even the predominant feature of those involved in active clashes with police. Neither of the two people killed by bullets on Wednesday morning were ethnically Ukrainian. But it is clear that the popularity of Pravy Sektor is growing and that many of those lobbing molotov cocktails and preparing for all-out battle are influenced by their ideas.

Tarasenko said it was hard to say how many active members of Pravy Sektor there were, but noted that its page on the social network Vkontakte had more than 50,000 members. On the barricades, "hundreds are quickly turning into thousands", he claimed.

As the clashes have continued, the international community has continued to put strong pressure on Yanukovych to avoid violence, but in recent days there has also been an acknowledgement of the darker side of the protest movement. A US state department statement issued on Wednesday blamed Yanukovych for the violence but added: "The aggressive actions of members of extreme-right group Pravy Sektor are not acceptable and are inflaming conditions on the streets and undermining the efforts of peaceful protesters."

Even amid the violence, there is a certain orderliness and purpose of mind to the protests. While a small number of buildings have suffered from the flames of the burning barricades, there has been no wholesale looting or random violence. Despite the fact that for two months people have been out on Independence Square protesting against Ukraine's move towards Moscow, a branch of Sberbank – a Russian state-controlled bank – which is adjacent to one of the entrances to the square has remained completely untouched, its glass facade undamaged.

But the number of people wielding baseball bats, planks of wood, golf clubs or even hammers has dramatically increased. There have been other disturbing scenes, such as when protesters captured groups of paid-for government thugs earlier in the week, and forced them to speak Ukrainian or sing the national anthem under duress, making videos of them and issuing threats.

The majority of protesters are horrified at the bloodshed and would be satisfied with some kind of compromise agreement, or at least willing to accept it to rule out the chance of further violence.

But Pravy Sektor says that if Yanukovych does not resign, he should be forced out.

"We would give him and his family 24 hours to leave the country, or there would be a revolutionary tribunal," said Tarasenko. Asked what he thought the most likely medium-term outcome of the clashes would be, he said: "Prolonged guerrilla warfare."

• Additional reporting by Oksana Grytsenko