In recent weeks, President Emmanuel Macron of France, who has seen deadly knife attacks in Paris and Nice on suspicion of Islamist motives, issued a statement expressing shock and sorrow.
We, the French, share the Austrians' shock and sadness following the attack in Vienna. It is a friendly nation, after France, that is under attack. It's our Europe here. It is necessary for our enemies to know who they are dealing with. We're not going to give in on anything,' he wrote.
Boris Johnson, the UK Prime Minister, also expressed his deep shock. He wrote on Twitter, "The UK 's thoughts are with the people of Austria-we stand united with you against terror."
The shooting was described by Canada's Justin Trudeau as "horrific and heartbreaking." "We condemn this act of terrorism in the strongest terms possible. Our thoughts are with the Austrian people and all those affected by this deplorable act.
In 1981, during an attack by two Palestinians at the same Vienna synagogue, two people were killed and 18 injured.
Mr. Kurz said that the Army would protect the capital's sites so that the police could concentrate on anti-terror operations.
"In our republic, we are currently experiencing difficult hours," Mr. Kurz wrote on Twitter.
"I would like to thank all the emergency forces who, particularly today, are risking their lives for our safety."
"With this repulsive terrorist attack, our police will take decisive action against the perpetrators."