Sydney hostages: Sydney gunman identified as Iranian
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Man Haron Monis, who received political asylum in Australia in 1996, was described by his former lawyer as an isolated figure.
Central Sydney is in lockdown as police surround the cafe, continuing negotiations with the gunman.
Several more hostages are said to have escaped after five got out earlier.
A black Islamic flag has been displayed at the window. The number of those held in the Lindt cafe is not clear.
The building is located in Martin Place, a busy shopping area in Sydney's financial district.
It appears the gunman has used three of the hostages to pass on demands, making them stand beside a black flag and having them make statements to a camera.
Prime Minister Tony Abbott said it was "profoundly shocking" that people were being "held hostage by an armed person claiming political motivation".
Offensive letters
Mr Monis, who styles himself as a Muslim cleric, is currently on bail for being an accessory to the murder of his former wife and is facing more than 40 sexual and indecent assault charges.
He has also been convicted of sending offensive letters to the families of deceased Australian soldiers.
"His ideology is just so strong and so powerful that it clouds his vision for common sense and objectiveness," his former lawyer, Manny Conditsis, said.
There are reports that one of his demands is for the flag of the Islamic State (IS) militant group to be delivered to the cafe, the BBC's Jon Donnison reports.
Shortly after the siege began people thought to be employees and visibly distressed could be seen holding up to the window a black flag bearing a declaration of the Islamic faith in Arabic. This was not, however, an IS flag.
The BBC has seen no claim of responsibility for the hostage-taking by IS or any other recognised jihadist group.
News organisations say the gunman contacted them to issue demands, which police urged media not to report.
Lights inside the cafe were turned out as night fell.
The incident began as people arrived for work in Martin Place early on Monday. Witnesses saw a man with a gun walk into the Lindt chocolate shop and cafe.
About 10 employees and 30 customers were thought to be inside at the time, Lindt said. Nearby offices were evacuated.
Police were due to interview them once the condition of their health had been assessed.
At the scene: Wendy Frew, BBC News, Sydney
The atmosphere in Martin Place itself was surreal. Office workers who had been evacuated from their buildings, construction workers from building sites and tourists packed the pedestrian plaza one block away from the Lindt coffee shop.
Rosemary D'Urso Healion had just come out of the Martin Place subway station and was walking to her office when she saw that it was blocked by police. Then she saw the police close down the subway station.
"I work in that building [where the siege is taking place] and I was just about to go in," she told the BBC, adding that she had been in contact with some of her colleagues who were in the building but not being held hostage.
She remained at Martin Place anxiously watching a police operation that appeared to be aimed at getting some of her colleagues out via a ladder erected on a window ledge on the first floor.
Martin Place is home to the state premier's office and the headquarters of major banks.
In September Australia - which has sent fighter jets to join the US-led coalition conducting air strikes against Islamic State in Iraq - carried out a big anti-terror raid.
One man was charged with plotting to behead a member of the public in Martin Place.
In October, the Australian parliament approved new anti-terrorism laws, including a provision designed to stop Australians fighting in overseas conflicts.
The black flag
A black flag bearing the white Arabic text of the "shahada", the basic statement of the Islamic faith, is used by jihadist groups worldwide
- The statement says: "There is no God but Allah, and Muhammad is his messenger"
- A black flag was the battle flag of the Prophet Muhammad and was carried into battle by many of his companions
- Today, it is used as a symbol of engagement in jihad, in the sense of holy war, by militant groups including al-Qaeda and Islamic State
- Islamic State's banner - unlike the flag raised in the window of the coffee shop - bears the first part of the shahada and the seal of the Prophet below it.
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