Man Haron Monis, the Iranian-born self-styled cleric who died along with two of the people he had taken hostage, was being investigated over fraud charges when he fled in 1996, police said.
But Iran's deputy foreign minister for Asia and Oceania affairs, Ebrahim Rahimpour, said Australia ignored the guidance sent.
"Despite several notifications to the Australian government regarding his criminal background, no attention was paid," Rahimpour told state television late Tuesday.
"We provided information and asked them to watch this person but unfortunately they did not pay attention.
"The Australian government acted very poorly as far as security and protective standards were concerned."
Australian Prime Minister Tony Abbott on Wednesday ordered an urgent inquiry into why Monis, a 50-year-old who was facing serious charges but out on bail, was not under surveillance and how he obtained citizenship.
Iran's police chief, Esmail Ahmadi Moghaddam, said Monis was known as Manteghi and managing a travel agency when he fled in 1996, leaving behind a wife and two children.
He travelled first to Malaysia and then on to Australia where he landed as a refugee but later obtained citizenship. An extradition request from Tehran in 2000 was unsuccessful, Moghaddam said on the Iranian police website.
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Australian officials sent the gunman's fingerprints to Tehran after the deadly siege, Moghaddam said, but because Iranian police do not have his prints on file other checks may be carried out.
"We are prepared for a joint investigation and, if they send us his DNA, we can compare it with his family to see if he is that person or not."
Australian officials say Monis had a history of extremism and violence, and faced charges including sex offences and abetting the murder of his ex-wife.
Last month, he posted a message in Arabic on his website pledging allegiance to "the Caliph of the Muslims", which some have interpreted to mean the leader of the Islamic State group, which has seized swathes of Iraq and Syria.
Yet he was allowed to roam free.
Monis took 17 hostages at a cafe in the heart of Sydney on Monday, unfurling an Islamic flag during a 16-hour siege.
Police eventually stormed the cafe leaving Monis and two hostages dead. Six others were wounded.
Monis, whom Abbott called "a madman", was well known to both state and federal police as well as the domestic intelligence agency ASIO, but was not on any Australian counter-terrorism watch lists.