The newly elected mayor of Budapest has vowed to prove to the rest of Europe that there is more to Hungary than the politics of its far-right prime minister, Viktor Orbán.

Gergely Karácsony, 44, who stood on a platform of a greener and fairer Budapest, won Sunday’s election with more than 50% of the vote, beating Orbán’s candidate despite a concerted campaign against him in government-friendly media and a threat that some federal funding would be withdrawn if Karácsony won.

The opposition also won a number of other Hungarian cities, in the first electoral setback for Orbán in more than a decade. Orbán’s Fidesz won its third consecutive term in office at parliamentary elections last year and controls much of the country’s media landscape.

“We have destroyed the myth that Fidesz is unbeatable, and this has massive significance for the whole country,” Karácsony said in an interview on Thursday morning at a central Budapest cafe before he cycled to city hall for an official handover ceremony.

Karácsony said once he took office he would increase cooperation with the liberal mayor of Warsaw, Rafał Trzaskowski, and other central European mayors to counterbalance the confrontational stance that Hungarian and Polish governments have taken with Brussels in recent years.

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“The governments of these countries are taking us away from the core of Europe, when this is the region that should be the most interested in not having a two-tier Europe,” he said.

On his first day in office on Friday, Karácsony plans to send two letters, one to Orbán asking for a meeting, and the other to the rector of Central European University asking the institution to keep as many courses as possible in Budapest.

The university, which teaches master’s degrees in English to students from across the world, has been forced to move some of its courses to Vienna after the government refused to accredit it to issue US degrees in Hungary. The university was founded by the billionaire financier and philanthropist George Soros, whom Orbán’s government has depicted as an enemy who wants to destroy the country.

Karácsony said that while he had no power to change the legal framework, he would assure CEU it was welcome in the city and would propose the establishment of a new scientific academy devoted to research and innovation based at the university.

He said he and Orbán’s government would look to see if there was a way to work together. “My political philosophy is all about compromise and building consensus. Sometimes I wish I was a politician in a Nordic country where you could govern by consensus, but now my job is to fight for peace,” he said.

While he wanted a constructive relationship, there were values he would not compromise on, and he said if Fidesz decided to go down the route of confrontation, “we are ready to pick up the gauntlet”.

He said priorities for his first year in charge were to improve the social safety net for low-income families, divert more funding to homeless shelters and make improvements to public transport. He has promised to boost Budapest’s green credentials and to attend the city’s annual pride march.

Pro-government media has claimed Karácsony only won with the votes of foreigners living in Budapest. Orbán has downplayed the results, pointing to a strong showing in the countryside and a small increase in the number of votes gained by Fidesz overall. Zoltán Kovács, Orbán’s spokesman, wrote on his blog in the aftermath of the result: “Winning more than 50% of all votes, [Fidesz] has once again shown that it’s still by far Hungary’s strongest political force.”

However, analysts say wresting the capital from Fidesz’s control will be a huge psychological boost for the Hungarian opposition, riven by years of infighting and irrelevance. The next nationwide elections are due in 2022.

Karácsony said people in Budapest and other big cities were no different to other Hungarians but had access to “a totally different media landscape” that helped to puncture government propaganda.

Additional reporting by Flora Garamvolgyi.