The leader of Austria's far-right Freedom Party, or FPO, says its unprecedented success in the country's parliamentary election has "opened the door to a new era", after provisional results showed it to be short of an overall majority, but winning the largest share of the votes.

Herbert Kickl's party won 29.2 percent of the vote, with the mainstream conservative Austrian People's Party, or OVP, which is the party of the country's Chancellor Karl Nehammer, securing 26.5 percent.

That was enough to give the FPO 56 seats in the 183-seat parliament, ahead of the OVP's 52, and 41 for the Social Democrats.

Turnout was high, at almost 75 percent, with the campaign being dominated by issues of migration and asylum, as well as the impact of the Russia-Ukraine conflict.

The FPO, whose first leader in the 1950s was a former Nazi officer, is a Euroskeptic far-right party.

Kickl, who has aligned himself with the right-wing prime minister of neighboring Hungary, Viktor Orban, and called him a role model, had promised voters he would build "Fortress Austria", and as results emerged, he praised them for their "optimism, courage and trust" in delivering a "piece of history".

Other right-wing leaders across Europe were quick to congratulate Kickl on his party's triumph.

Alice Weidel, co-leader of Germany's Alternative for Deutschland, shared a picture of them together, and Marine Le Pen, of France's National Rally party, said the result was part of a Europe-wide "groundswell (of support) carrying the defense of national interests", leading to "people's triumphs everywhere".

The Netherlands right-winger Geert Wilders said it was more proof that millions of people across Europe were voting in support of "identity, sovereignty, freedom and no more illegal immigration/asylum", and that times were changing.

Kathrin Stainer-Haemmerle, a political science professor at the Carinthia University of Applied Sciences, told Reuters that Austria's role in the European Union would be "significantly different" if Kickl did manage to become chancellor.

The FPO now has the upper hand in forming a coalition government, although it would not be a straightforward process, and President Alexander Van der Bellen, who oversees the formation of governments, has previously been critical of its policies.

"We don't need to change our position, because we have always said that we're ready to lead a government, we're ready to push forward this change in Austria side-by-side with the people," Kickl said in a television appearance alongside other party leaders. "The other parties should ask themselves where they stand on democracy."

The party has been in coalition before, but not as the dominant party, and the OVP has refused to join any government potentially headed by Kickl, with Nehammer saying it is "impossible to form a government with someone who adores conspiracy theories".