EU chief calls for body 'to train imams'
"It is very important to be firm on this. I think, for example, that we should have a debate at the European level connected to the idea that was raised some time ago to set up a European institute to train imams," he told the media.
Michel said "this message of tolerance, openness can be conveyed at the European level ... to ensure that the primacy of civil law is accepted," he said.
"Online messages glorifying terrorism must be quickly removed. There must be no impunity for terrorists and those praising them on internet," he said later in a tweet.
Last Monday's shooting was the first major attack of its kind in Austria for decades and the first blamed on a jihadist.
The gunman was identified as Kujtim Fejzulai, 20, a dual Austrian-Macedonian national who was convicted and imprisoned last year for trying to go to Syria to join Islamic State group.
"We think that this terrorist threat is a fundamental, grave, serious threat against the values" of modern Europe, Michel said, adding that "we have no intention of showing any weakness or laxity".
The attack in Vienna comes amid weeks of heightened tensions between Europe and the Muslim world after remarks made by French President Emmanuel Macron on free speech and Islam.
The comments have catapulted Macron to the centre of controversy in a revived debate about freedom of expression, Islam and France's treatment of its Muslim minority groups.
The French president recently defended the re-publishing of cartoons of the Prophet Muhammad, sparking a backlash from Muslims around the world.
He has also been accused of persecuting Muslims in France, with French authorities currently cracking down on Muslim NGOs under a new 'separatism' law that has been criticised as curtailing civil liberties.
The issue of religious extremism has come to the fore as France reels from 16 October beheading of teacher Samuel Paty by a suspected Islamist radical from Russia's region of Chechnya.
Read more: European Islamic institutions send bold 'open letter to President Macron'
The teacher had shown a class a cartoon of the Prophet Muhammad in the wake of the controversy generated by their reprinting by satirical magazine Charlie Hebdo to mark the beginning of the trial of suspects over the massacre of its staff in January 2015.
Even before that attack, Macron had promised a tough new campaign against "Islamism" which had aroused controversy and condemnation from Muslims around the world.
Protests against Macron’s perceived Islmophobia erupted across the Muslim world, including Afghanistan, Pakistan, Bangladesh, Mali, Mauritania, Lebanon and Yemen.
World leaders have also weighed in on the matter, with Macron and Turkish President Recept Tayyip Erdogan trading barbs and insults.
Agencies contributed to this report.