The Austrian Chancellor, Sebastian Kurz, has pulled the plug on his coalition with the far-right Freedom Party after a damaging video prompted its leader to step down as vice chancellor.

"Enough is enough," Mr Kurz said in a statement to the media, listing several lesser scandals involving the Freedom Party that did not cause their coalition to collapse.

He said he would propose to Austrian President Alexander Van der Bellen that a snap election be held as soon as possible.

Austria's vice chancellor and longtime far-right leader, Heinz-Christian Strache, announced he was stepping down over "catastrophic" video footage that shows him meeting a woman posing as the niece of a Russian oligarch in 2017, shortly before the election that brought him to power.

Mr Strache described the sting as a "targeted political assassination" that never led to any money changing hands, insisting the only crime that took place was illegally videotaping a private dinner party.

In the footage published by German media yesterday evening, a week before European Parliament elections, he appears to offer to funnel contracts towards a company in exchange for political and financial support.

"It was dumb, it was irresponsible and it was a mistake," Mr Strache told a news conference, fighting back tears as he asked his wife and others to forgive him.

"In the cold light of day, my remarks were catastrophic and exceedingly embarrassing," he said about the video, in which he also referred to party financing rules and how to work around them, but also insisted on having to act legally.

Mr Kurz has repeatedly distanced himself from the FPO over lesser scandals, mostly ones involving party officials and anti-Semitism or racism, to protect his popularity.

"This is the tip of the iceberg," Thomas Drozda, from the opposition Social Democrats, told national broadcaster ORF.

"I expect the chancellor, who evidently has known about this video for 48 hours, and that his coalition partner is drowning in a swamp of corruption, to speak and explain his position. He has been hiding for 48 hours ... he owes the country an explanation."

In an at-times rambling defence of his behaviour, Mr Strache also apologised for flirting with the woman, whom he describes as attractive in the recording.

"It was typical alcohol-fuelled macho behaviour in which, yes, I also wanted to impress the attractive female host and I behaved like a bragging teenager," he said.

Mr Strache said he would be replaced by Transport Minister Norbert Hofer, his deputy within the party who narrowly lost 2016's presidential election and is more popular than the sometimes aggressive and abrasive Mr Strache.

"I do not in any circumstances want my wrong behaviour to provide a pretext for the government to collapse," Mr Strache said.

Opposition parties including the liberal Neos party and the Greens called for a snap election.

A crowd of thousands with left-wing placards and banners gathered on the square outside Mr Kurz's office, chanting "Snap elections now!".

Police estimated their number at 5,000.