BERLIN — The Austrian president called on Sunday for new elections in September, a day after the government collapsed over the emergence of a video that showed the country’s far-right vice chancellor promising favors to a woman who claimed to be a Russian investor.

The revelations led thousands to take to the streets of Vienna on Saturday to demand new elections. And on Sunday, the president, Alexander Van der Bellen, said the country had “exact rules and procedures” to handle the crisis that ensued after Chancellor Sebastian Kurz said that he could no longer work with the Freedom Party, led by Vice Chancellor Heinz-Christian Strache.

“Based on these constitutional rules, I will ensure stability, calm and continuity are of the highest priority,” Mr. Van der Bellen said in a statement after meeting with Mr. Kurz. “Consequently, I urge there to be new elections in September, if possible at the beginning of the month.”

Mr. Strache resigned after the German newsmagazine Der Spiegel and the newspaper Süddeutsche Zeitung on Friday released the video, which was filmed months before the 2017 election, in which Mr. Kurz led his party to victory. Norbert Hofer was chosen to temporarily replaced Mr. Strache as head of the Freedom Party.