In a statement posted on Twitter late Monday night, Kurz said the military would take over some police duties in order to let officers concentrate on chasing down the perpetrators of a series of shootings across the capital in which more than a dozen people have been wounded.
"We will never allow ourselves to be intimidated by terrorism and will fight these attacks resolutely by all means," Kurz said.
"The whole country is thinking about the victims, the injured and their families, to whom I express my deepest condolences," he continued. "We thank the leaders of the European Union and our international partners for their sympathy and the expressions of solidarity."
On Monday evening, at least 15 people were shot by possibly up to seven perpetrators in a series of shootings across the capital city that began near the city's main synagogue. One of the victims, a police officer, has died of his wounds, and another seven have serious injuries, according to local media.
There had been reports of hostage-taking, but a spokesperson for the Akakiko restaurant refuted those claims in a comment given to Sputnik.
Police in Vienna have recommended people stay away from public places, as not all the perpetrators have yet been found. However, one was shot to death by police.
The incident comes in the wake of a series of attacks across France in recent weeks that has seen three killed in Nice and a man killed in a Paris suburb. The attacks have been prompted by a series of offensive caricatures of the Muslim prophet Mohammad.