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.

The downfall of Mr. Kurz’s right-leaning coalition government, just 17 months after taking office, fueled suspicions about how much far-right parties were willing to let Russia get involved in national politics. And it came a week before elections for the European Parliament, in which far-right movements across the Continent were poised to weaken support for more moderate and established parties.

But with months remaining until a new national Parliament is voted in, it is too early to tell who will ultimately benefit from the Austrian scandal, analysts said.

Questions also remain about how Mr. Kurz will be able to govern in the months before the new national elections, with opposition figures and members of his own conservative People’s Party calling for all Freedom Party ministers to quit their posts. The most important of those is the interior minister, Herbert Kickl, who is responsible for the country’s security apparatus.

Pamela Rendi-Wagner, leader of the opposition Austrian Social Democrats, said in a statement to The New York Times on Sunday that Mr. Kurz “had his chance and lost it.”

“Now he is not even able to ensure a stable transition,” she added. “As a first step, the three ministries of justice, interior and defense must immediately be filled with independent experts. It’s the only way to ensure a complete and independent investigation.”

In a video posted on Facebook a day after the vice chancellor’s resignation, Mr. Hofer seemed to open the door to leaving the coalition

“My dear friends, I will do everything to make sure that the FPÖ remains a strong party, whether as part of the government or in opposition.” he said, using the German initials for the Freedom Party.

He also noted that Mr. Kurz had demanded that Mr. Kickl resign as interior minister.

Mr. Kickl shot back at the chancellor in a Facebook post on Sunday, saying that although Mr. Kurz had said the coalition ended for the good of Austria, “the past hours and days show that is not true.”

“Chancellor Kurz and his conservative party are only concerned with power,” Mr. Kickl wrote, “apparently at any price, even blowing up the coalition, which the people have held in highest respect for their work.”

The video that led to the collapse of Mr. Kurz’s governing coalition had been filmed in a villa on the Spanish island of Ibiza three months before the 2017 Austrian elections in which Mr. Kurz led his party to victory. It showed Mr. Strache promising infrastructure contracts to a woman who claimed to be the niece of a Russian oligarch in return for support for his Freedom Party and her offer to invest 250 million euros, around $280 million, in Austria.

Mr. Strache also suggested undermining the independence of Austria’s news media. The New York Times could not independently verify the contents of the entire video.

The revelations followed a series of missteps by the Freedom Party since joining the coalition, such as a raid on the country’s own domestic intelligence service, verbal attacks on the news media and a poem comparing immigrants to rats. And they raised new concerns about whether a party inside government had been working to undermine liberal democracy and press freedom in Austria.

“It might be better for the FPÖ if they are no longer in the ministries,” said Laurenz Ennser-Jedenastik, a political scientist at the University of Vienna. Like other experts, Mr. Ennser-Jedenastik said he believed that the Freedom Party might avoid major damage if it ran a convincing campaign in the coming months.

Peter Filzmaier, an Austrian political scientist, told the public broadcaster ORF that everything was “up to the president,” adding that Mr. Van der Bellen “needs to name someone to take over the agenda of the vice chancellor.”

“Mr. Kurz’s calculus is clear,” Mr. Filzmaier told The New York Times. “If the FPÖ loses many voters, who else are they going to vote for?” He explained that for the conservative voters disillusioned with the far-right Freedom Party, Mr. Kurz’s more mainstream party was the only game in town.

Mr. Filzmaier and other analysts did not predict a radical change in voter preference among the parties, unless something surprising happens in the long run-up to the vote.

In the fall, Mr. Kurz may face the same tough decision if his party comes out ahead, as current polls predict it would, but fails to gain a majority of votes in government.

“The chance of the same version of the current coalition government occurring isn’t very high, but it grows dramatically if the FPÖ does very badly,” Mr. Ennser-Jedenastik said.

Christopher F. Schuetze reported from Berlin, and Melissa Eddy from Copenhagen.



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