As Ukraine's street protests against corruption grow increasingly ugly, the unlikely figure of heavyweight boxer Vitali Klitschko has emerged as a voice for the opposition. What will happen next – and why has he taken on the biggest fight of his life?

People have been trying to land kicks and punches on Vitali Klitschko for most of the past two decades, and he has brushed almost all of them off with ease. But his current opponent, Ukrainian president Viktor Yanukovych, has a few advantages that none of the previous challengers possessed: several thousand riot police at his disposal, for a start, and the use of a pliant court system to prevent Klitschko from entering the ring in the first place.

Klitschko, whose PhD in sports science combined with a fearsome reputation as a former heavyweight champion earned the 42-year-old the nickname "Dr Ironfist", has emerged as the natural leader of the street protests that have swept Ukraine for the past two months, ever since the president went back on his promise to sign an association agreement with the EU. Crowds, mainly from the pro-European west of the country, were initially drawn to stand up for their desires of European integration, but the rallies soon morphed into general discontent with the bloated kleptocracy that critics say surrounds the president. Barricades were erected around Independence Square, and every day for two months, politicians including Klitschko have addressed crowds from the stage, rallying the masses in protest against the president he eventually hopes to succeed. Klitschko has his hands full trying to contain the protest movement which erupted into violence on Sunday night, as thousands hurled rocks at riot police and set their buses on fire. Klitschko was moving through the crowds, unsuccessfully calling for calm, and at one point was even sprayed in the face with a fire extinguisher by an angry protester.

But despite the difficulty and complexity of the task ahead, Klitschko is resolutely confident that the protests, which have so far failed to draw any major concessions from Yanukovych, represent a victory for the Ukrainian people.

"People are saying: 'We don't want to live like this. We want things to change,' he tells me just days before the mood turned violent. "This is a victory in the head of every Ukrainian, and in their heart – and this is worth an awful lot."

Dressed in a dark grey suit that sits surprisingly elegantly on his enormous frame, Klitschko speaks slowly and methodically.

"The system today is built to service the clan, the family, and not society as a whole. Yanukovych doesn't want change. He says he does. But he says he wanted European integration and that turned out to be a con."

He pauses, blinking, before answering each question, usually with carefully formulated and somewhat monotonous answers. Would he put Yanukovych on trial for the corruption that has escalated under the current regime, and the blatant enrichment of his family members? Klitschko pauses. "If people break the law, they should be punished," he says. So is that a yes? What does he personally think about Yanukovych? He pauses again. "If people break the law, they should be punished." It is as though he has discovered the concept of speaking like a politician, but not yet mastered the craft.

He might lack the fiery charisma of born political leaders, but in a country where the 2004 Orange Revolution was followed by huge disappointment, and people are all too used to broken promises from politicians, Klitschko's plodding sincerity and political neophytism are attractive qualities. Unlike many Ukrainian politicians, he is free from allegations of corruption. The expensive watch on his wrist and the smart cars he drives can be accounted for by the millions that he earned in transparent fashion in the boxing ring.

Klitschko's boxing statistics are extraordinary. He won 45 of 47 professional fights, and was never knocked out once. Boxing aficionados suggest that the time of his dominance was not a particularly glorious era for the sport and that he never faced a truly brilliant challenger, making him a boxing equivalent of Pete Sampras – repeatedly victorious yet not destined to be remembered as one of the all-time greats. Nevertheless, along with his younger brother, Vladimir, he has completely dominated the sport for a decade.

Klitschko's father was a Soviet military pilot, and the young Vitali grew up on military bases across the former Soviet Union, moving from the Central Asian steppes to the Baltic before settling in Kiev in 1984 as a teenager. With its chiselled features and sombre expression, Klitschko's face could come from a Stalin-era poster extolling the Soviet sporting hero,and his aura of moral grounding and sincerity certainly came across during his boxing career. He cut an unusually polite figure in a milieu normally associated with hubris and puerile bravado. Klitschko recalls a fight against Briton Richard Vince, in Norwich, back in 1994. It was before he had become boxing world champion and was instead tearing up the kickboxing circuit, and he travelled to Britain for a world title fight in the sport.

"The whole family of my opponent came to the fight and were sitting in the front row. His dad, mum, wife and kids were there. I knocked him out in the second round and he blacked out. He was lying there unconscious, and I saw pain in the eyes of his family. After that I said that my relatives should never come to my fights. I don't want to cause those emotions in my family." He also says he sought out Vince's relatives and apologised to them after the fight. When his brother Vladimir, five years his junior, also became a successful heavyweight boxer, he promised his mother that the pair would never fight each other.

Klitschko, center, is attacked and sprayed with a fire extinguisher as he tries to stop clashes. Photograph: Efrem Lukatsky/AP

I try my hardest to steer clear of hackneyed comparisons between the boxing ring and the Ukrainian political fight, but Klitschko himself repeatedly wheels out the metaphors. Even the name of his political party, the Ukrainian Democratic Alliance for Reform, handily condenses into the acronym Udar, the Russian and Ukrainian word for "punch".

When I ask whether he feels uneasy sharing a stage with Oleh Tyahnybok, the hardcore Ukrainian nationalist known for his antisemitic outbursts, he raises a supersized hand in front of him and curls it into a fist.

"In order to land a punch, you need to bring your fingers together into a fist. We need to join all of our forces together. That is the only way that we can win."

Klitschko and Tyahnybok have been joined on the stage by Arseniy Yatsenyuk, the representative of jailed former prime minister Yulia Tymoshenko's Fatherland party.

"Three things unite us," says Klitschko of the troika of opposition leaders. "The first is disagreement with the current economic situation; the second is that we see European integration as the only future for Ukraine, and the third is the struggle against the current authoritarian regime."

Tymoshenko, who was one of the leaders of the Orange Revolution, was considered Yanukovych's most dangerous potential enemy before the emergence of Klitschko, and most people believe her jailing was a political decision. However, Yatsenyuk lacks the charisma of his party leader, and with his spectacles and roll-neck jumpers looks more like a linguistics professor than a rousing political leader.

With Tyahnybok's appeal limited to the more nationalist west of Ukraine, most people assume that if the opposition puts forward a united candidate to take on Yanukovych in presidential elections, Klitschko is the only viable choice to appeal to a broad demographic. The vote is scheduled for 2015, though one of the key demands of the protests from the start has been early elections.

The government has attempted to bar him from any future presidential race by introducing a new law that would disqualify him due to his extended absences from the country while he pursued his boxing career. He was resident in Germany for a long period, and recent rumours in the Ukrainian press say he also has a US social security number and pays US taxes. The boxer, who suddenly starts referring to himself in the third person, says the new electoral law is a nonsense.

"The idea is deliberately being fed to society that Klitschko can't stand. I have always been a citizen of Ukraine since the moment of our independence. I was registered in Ukraine and I live in Ukraine. But sport is global, and everyone knows that you can't limit yourself to one country. The authorities are doing everything to ensure Klitschko can't stand in elections. But I will say it once again: there are no reasons to remove me from the elections."

When I ask what he will do if he, nevertheless, is banned from standing, he is evasive, saying he will "defend his position firmly". What does this mean? "My position is clear to everyone … and I am certain that they won't do something so stupid. It would be the same as saying that ice is warm or water is dry." Yanukovych's government has made its fair share of decisions that many might regard as stupid over recent months, I point out.

Klitschko, right, lands a punch on Britain's Dereck Chisora during a title bout in 2012. Photograph: Frank Augstein/AP

"Then I will fight it. This is a battle, and I don't plan to give up easily."

The question of just how far he is willing to go in terms of violent opposition to a regime that has refused to listen to peaceful protest remains unanswered, but he is insistent that any violence is the fault of the authorities.

"The protest mood in Ukraine is at a higher temperature than ever before," says Klitschko towards the end of the interview. "We only need a small spark for the situation to develop in a way that will be completely out of control for the authorities."

His words turn out to be prophetic, as the rally on Sunday turned violent, with dozens of protesters and police injured, and the way out of the political impasse is now even more unclear. Klitschko will need to negotiate the landscape and make a decision on whether he goes for all-out war with the regime, or bides his time until a 2015 vote. He went to see Yanukovych on Sunday evening, where the president offered to start negotiations with the opposition leaders. However, on Monday, it was announced that Yanukovych himself would not attend the talks.

"Not signing the EU integration agreement, attacking peaceful protesters and ignoring human rights – all of these were indicators of the way things are in Ukraine right now. If these things keep happening, then nobody can predict how it will end."

Klitschko warned Yanukovych on Sunday night to "find strength and not repeat the fate of Ceausescu and Gaddafi", referring to the former Romanian and Libyan dictators who ended up dead. He added that if the government did not pull back from violence then "civil war cannot be ruled out". While the majority of protesters remain peaceful, it is clear that the radical element is growing, partly in reaction to new anti-protest laws which essentially make the street rallies that have paralysed the capital illegal.

Klitschko announced recently that he was retiring from boxing to concentrate on his political career. He has been given "champion emeritus" status, which would allow him to mount a challenge to any new champion at any time, but he says that such thoughts are far from his mind at the moment.

"I am thankful for this title of champion emeritus, and proud I never lost my title. A lot of people want to see a last fight, but I am now engaged in a different fight. One that is much harder, much more vicious and much more important to me. I am fighting for democracy, and fighting for Ukraine."