Hungarian voters in the country's capital, Budapest, have handed the ruling Fidesz party their biggest electoral setback in a decade.

In the city's tightly contested mayoral race, Gergely Karacsony defeated the incumbent, Istvan Tarlos, who was running on the Fidesz ticket and had the backing of Prime Minister Viktor Orban.

With over 80% of votes counted, Karacsony, a former political scientists, had 51% of the vote compared with Tarlos at around 44%.

Karacsony ran as a candidate backed by a coalition of left-leaning parties. 

"A unified opposition that voters have long expected has been formed, and the result tells us this is the path to take onwards," Karacsony told his supporters. 

This mayoral election is seen by many political analysts as a significant breakthrough for an opposition that has struggled to get a foothold on Hungarian politics since the conservatives came to power nine years ago. While the result has little baring on Orban's grip on power at a national level, Budapest is home to around a fifth of the country's population and accounts for roughly a third of its economic output. 

Opposition candidates enjoyed success in a number of Hungary's urban areas. They won 10 mayoral races in the country's 23 biggest cities. That's compared with just three won back in 2014.

Some believe this result mirrors recent local elections seen in Poland and Turkey where opposition parties performed well against the ruling parties in local elections. 

"Changing Budapest and the major cities is the first step toward changing Hungary," Budapest's new mayor said. 

"We will take Budapest back to Europe," he added in a post on Facebook.

Sunday's municipal election saw over 3,000 mayoral spots and over 17,000 local council member positions up for grabs. While opposition parties won some major seats, Fidesz showed they still retain large support throughout the country, especially in more rural areas.

"On the national level, the result is nice, but in Budapest, there is thinking to be done," said Budapest's outgoing mayor, Tarlos, at a news conference.

Orban's Chief of Staff described the election as "a dirty campaign". Fidesz which heralds itself as a Christian-conservative party, attacked Karacsony for being pro-migration. But ahead of the election, Fidesz was hurt by a sex scandal involving the incumbent mayor of Gyor, Zsolt Borkai. He managed to retain his seat but some political analysts feel it hurt the party so close to elections. 

Despite the bitter campaign, there were messages of reconciliation after the vote. 

"We acknowledge this decision in Budapest, and stand ready to cooperate," Orban said at a rally.

Opposition parties in Hungary see Budapest's mayoral race as a blueprint for future political success. But they'll have to wait until 2022 before getting the chance to take on Viktor Orban and Fidesz in a general election.