VIENNA (Reuters) -Austria's next general election will be held on Sept. 29, at the end of the current five-year parliament, Chancellor Karl Nehammer said on Tuesday, deferring a showdown with an emboldened far-right for as long as possible.

Polls show the far-right Freedom Party (FPO) with a clear lead over its rivals, capitalising on voter dissatisfaction with the ruling coalition of Nehammer's conservatives and the Greens, which has been fuelled by crises ranging from the COVID-19 pandemic to inflation far above the euro zone average.

The anti-immigration FPO won European elections in Austria for the first time on Sunday, albeit by a margin of under one percentage point over Nehammer's People's Party (OVP), and less than polls and an election-night forecast had suggested.

"At tomorrow's cabinet meeting, Sept. 29 will be set as the date of the National Council elections," Nehammer said on social media platform X, referring to the lower house.

Austria's short one-month campaign will pit centrist parties against the far-right, echoing the clash of values French President Emmanuel Macron described in an address on Sunday in which he announced he was dissolving parliament and calling a snap election due to a surge in support for the far-right.

"I can promise voters that I have understood the message," Nehammer told reporters on Sunday night when it was clear the FPO had won the European parliamentary election. "There is a great deal of dissatisfaction that was visible today."

Since they would have likely lost seats in any snap election, Nehammer's OVP and the Greens were effectively condemned to work together until the end of this parliament despite bickering over key issues like immigration, and repeated bouts of speculation that a snap election was imminent.

That speculation faded recently and it became widely expected that parliament would run its course. That was all the more remarkable given that Austrian coalitions often collapse and the Greens even forced Nehammer's predecessor Sebastian Kurz from office over a corruption scandal in 2021.

Austria has had six chancellors in the past 10 years and one of them, Kurz, held the office twice. Kurz denies wrongdoing.

Polls for the parliamentary election show the FPO on around 30% with the OVP and the opposition Social Democrats competing for second place on around 20%. Forming a coalition could be complicated since the leaders of all five parliamentary parties have ruled out a coalition with FPO leader Herbert Kickl.

"Today we have taken the first step," Kickl said in a speech to members of his party on Sunday night. "Now we have stay fully focused and launch the second phase, and the second phase is (securing) the chancellor's office."

(Reporting by Francois MurphyEditing by Peter Graff, Dave Graham, Alexandra Hudson)

By Francois Murphy