“After yesterday's video, I must say quite honestly, enough is enough,” Kurz told the media, listing a string of other minor scandals involving the Freedom Party (FPOe), adding that he would recommend to President Alexander Van der Bellen that snap elections be held as quickly as possible.
"Even if I didn't express myself publicly at the time, there were many situations that I found difficult to swallow," Kurz said of his time in government with the FPOe since December 2017.
He said the party was damaging Austria's reputation abroad and that meetings with FPOe representatives on Saturday had left him with the impression that it was not prepared to make the changes necessary to stay in government.
Vice-chancellor Strache, a key figure of the European far-right, announced his resignation on Saturday following revelations that he had promised public contracts in return for help from a fake Russian backer during his campaign in the 2017 parliamentary elections.
Strache denounced what he called an illegal "targeted political attack", but said he would quit in order to avoid further damage to the government.
Germany's Der Spiegel and Sueddeutsche Zeitung released hidden video footage of a sting operation allegedly filmed at a luxury villa on the Spanish island of Ibiza, months before Austria's 2017's elections.
Strache and his Freedom Party's group leader in parliament, Johann Gudenus, are seen in duscussions with a woman purporting to be the niece of a Russian oligarch, who says she wants control of Austria's largest-circulation tabloid, the Krone Zeitung.
Strache is seen suggesting that new owners could make staff changes at the Krone and use the paper to help his Freedom Party in its election campaign.