Several people have been taken hostage by at least one armed man at a Lindt cafe in the centre of Sydney.
Hundreds of armed police have sealed off the normally busy Martin Place in Sydney's central business district.
At least three people have been seen inside the cafe with their hands up against a window, and holding up a black flag with Arabic writing.
Australian Prime Minister Tony Abbott has described the incident as "deeply concerning".
He said it was not yet clear who was behind the incident but that it could be politically motivated.
In a news conference, he said the National Security Committee had been briefed, and urged Australians to go about their lives but to be alert.
"I can think of almost nothing more distressing, more terrifying than to be caught up in such a situation, and our hearts go out to these people," he said.
New South Wales Police said in a statement that an "armed incident" was under way, and that "specialist officers are attempting to make contact with those inside a cafe".
The police said nearby offices had been evacuated as a precaution and asked people to remain indoors and away from open windows.
Martin Place is a public pedestrian thoroughfare through the heart of Sydney, joining its parliamentary, legal and retail districts.
It is full of media, members of the public and the police, with what appear to be anxious colleagues of people trapped inside the building waiting for news. Several surrounding blocks are cordoned off.
Police are at this stage not giving media briefings at the site - dozens of police cars have arrived at the scene, with more continuing to come.
The incident began as people were arriving for work in Martin Place on Monday morning.
People evacuated from office buildings have gathered in nearby Hyde Park
Witnesses saw a man with a bag and gun walk into the Lindt chocolate shop and cafe. Police shut down the area, closing roads and moving people away. The Martin Place station was also closed.
The Lindt company said about 10 employees and 30 customers were thought to be inside.
Shortly after, television footage showed at least three people, thought to be employees of the cafe and who were visibly distressed, holding a black sign with the Islamic creed written on it up to the window.
The BBC's Security Correspondent Frank Gardner said the flag was similar to but not the same as that used by the Islamic State militant group in the Middle East.
Police have been escorting people out of nearby buildings
An Australian Broadcasting Corporation reporter said that gunfire had been heard at the scene - but this has not been confirmed.
No injuries have been reported from the incident, according to a police spokesperson.
Martin Place is home to the state premier's office and the headquarters of two of the nation's largest banks. The state parliament house is also only a few streets away.
Courts in the business district have been closed for the day, and a number of banks have said they will not open.
Australia's terror threat timeline
Terror threatPolice have also said that they are dealing with an "incident" at the Sydney Opera House, which has been evacuated.
People were evacuated from the Sydney Opera House on Monday morning after a suspicious package was found
Local media are reporting that a suspicious package was found there on Monday, though it was unclear whether it was related.
Speaking in Canberra, Mr Abbott said that the Martin Place incident was still unfolding, and urged caution. But he said the "whole point of politically motivated violence is to scare people out of being themselves".
"Australia is a peaceful, open and generous society - nothing should ever change that and that's why I would urge all Australians today to go about their business as usual," he said.
Australia has been facing a growing terror threat in recent months, in part connected to the fight against the Islamic State.
About 70 Australians are believed to be fighting for militant groups in the Middle East while another 20 have returned home.
In September, the largest anti-terror raids in Australian history were carried out in Sydney and Brisbane after intelligence emerged that people were planning to carry out random attacks on Australian soil. One person was charged with terror offences.
Anti-terror legislation was passed in October, which critics said was too severe. Mr Abbott has said the threat meant "the delicate balance between freedom and security may have to shift".
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