At least one "Islamist terrorist" was responsible for attacks across central Vienna, in which at least five people were killed and several others injured, Austrian Interior Minister Karl Nehammer said on Tuesday.
A massive search operation has been launched for other attackers, with at least 1,000 police officers fanning out across the city, a police spokesman said.
In an early morning televised news conference, Nehammer repeated calls for the public to stay off the streets.
Nehammer said police had shot dead one attacker, a man wearing an explosives belt that turned out to be fake, whom authorities have identified as an Islamic State sympathiser.
"We experienced an attack yesterday evening by at least one Islamist terrorist, a situation that we have not had to live through in Austria for decades," Nehammer said.
"Austria for more than 75 years has been a strong democracy, a mature democracy, a country whose identity is marked by values and basic rights, with freedom of expression, rule of law, but also tolerance in human coexistence," he said. "Yesterday's attack is an attack on just these values."
The assailant killed by police, and other potential gunmen, attacked six locations in central Vienna on Monday evening, starting outside the main synagogue. Witnesses described the men firing into crowds in bars with automatic rifles, as many people took advantage of the last evening before a nationwide curfew was introduced because of COVID-19.
Police confirmed on Tuesday that three civilians - two men and a woman - were killed in the attacks with at least 15 others wounded, including a police officer. Broadcaster ORF later said a fourth civilian, a woman, had died.
Nehammer said video material had been seized from the home of the known assailant during a search and police were investigating his potential connections.
News agency APA reported that multiple homes had been searched and arrests made, citing the Interior Ministry. An Interior Ministry spokesman was not immediately available for comment on the APA report.
Vienna's police chief declined to provide further details on the attacker's identity, citing potential endangerment of the investigation.
Police sealed off much of the historic centre of the city overnight, urging the public to shelter in place. Many sought refuge in bars and hotels, while public transport throughout the old town was shut down and police scoured the city.
Oskar Deutsch, the head of Vienna's Jewish community, which has offices adjoining the synagogue on a narrow cobbled street dotted with bars, said on Twitter that it was not clear whether the temple or offices were targeted but that they were closed at the time.
Videos circulated on social media of a gunman running down a cobblestone street shooting and shouting. One showed a man gunning down a person outside what appeared to be a bar on the street housing the synagogue.
Austria's capital had been spared the kind of deadly militant attacks that have struck Paris, London, Berlin and Brussels, among others, in recent years. Austria is part of the US-led Global Coalition to Defeat ISIS formed in 2014.
Condolences poured in from around the world, with top officials from the European Union, France, Norway, Greece and the United States expressing their shock at the attacks.
US President Donald Trump said in a tweet that "our prayers are with the people of Vienna after yet another vile act of terrorism in Europe."
"These evil attacks against innocent people must stop. The US stands with Austria, France, and all of Europe in the fight against terrorists, including radical Islamic terrorists."
Democratic presidential candidate Joe Biden condemned what he called a "horrific terrorist attack," adding, "We must all stand united against hate and violence."