German police shot dead the 18-year-old man on Thursday when he fired a vintage rifle at them near the diplomatic building.
They said they were treating it as a "terrorist attack", apparently timed to coincide with the anniversary of the killings of Israeli athletes at the 1972 Olympic Games.
Authorities raided the gunman's home in the Salzburg region, seizing electronic data carriers, Austria's top security chief Franz Ruf told a press conference in Vienna on Friday.
READ ALSO: Munich Israeli consulate gunman was 'Austrian national known to authorities'
During the raid, "no weapons or IS propaganda" material were found, Ruf added.
Despite being subject to a ban on owning and carrying weapons, the man managed to purchase a vintage carbine rifle fitted with a bayonet with around "fifty rounds of ammunition" for 400 euros ($445) the day before the attack, Ruf said.
He opened fire at around 9:00 am (0700 GMT) near the Israeli consulate, sparking a mobilisation of about 500 police in downtown Munich.
At a separate press conference in Munich, prosecutor Gabriele Tilmann said investigators were combing through the gunman's electronic data but had yet to find conclusive evidence of his motive.
But the "working hypothesis" was that "the perpetrator acted out of Islamist or anti-Semitic motivation", she told reporters.
Austrian police said on Thursday that the gunman, who had Bosnian roots, had previously been investigated on suspicion of links to terrorism.
Investigators last year found three videos he had recorded in 2021, showing scenes from a computer game "with Islamist content", prosecutors said in a statement.
In one of them the suspect had used an avatar with a flag of the "al-Nusra Front", a jihadist group active in Syria, said Ruf.
But the investigation was dropped in 2023 as there were no indications that he was active in "radical" circles, prosecutors said.
"The mere playing of a computer game or the re-enactment of violent Islamist scenes was not sufficient to prove intent to commit the offence," they added.
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