However, the director-general of the Australian Security Intelligence Organisation (Asio), Duncan Lewis, said there could be no guarantee of safety from extremist violence in the future.
Mr Lewis was speaking after the Paris attacks in which 129 people died.
The Islamic State (IS) militant group has said it was behind the attacks and warned of further violence.
Mr Lewis told Australian broadcaster ABC that while there was no evidence of a specific threat against Australia similar to the attacks in Paris, the number of potential threats had increased in recent years.
"We have had three attacks involving fatalities and six thwarted attacks in the past 12 months," he said.
"To put that in some sort of historic perspective, that represents just over a third of the attacks or planned attacks that we've had in this country over the last 15 years."
Asio - Australia's domestic security agency - increased the National Terrorism Public Alert Level from medium to high in September last year. This signifies that an attack is "likely".
Mr Lewis said this had been reviewed following the Paris attacks but that there were no plans to move it to the highest level of "extreme" which indicates an attack is imminent.
"If you consider there have been three successful attacks in Australia since that time, then I think that the threat level of 'likely' is most appropriate.
"We have no specific information leading us to believe there is any imminent threat of an attack presently, it is not appropriate for us to move the threat level to the next elevated position.
"This is very important for Australians to realise, we have no specific information about any particular attack planning in this country that would be reflective of what happened in France," he said.
In October. 15-year-old Muslim boy Farhad Jabar shot dead New South Wales police worker Curtis Cheng as the accountant left a police building in the Sydney suburb of Parramatta.
This came after the Sydney siege incident in December last year in which two hostages were killed, and the shooting of an 18-year-old man in Victoria who wounded counter-terrorism officers outside a police station.
Australia is part of a US-led coalition bombing IS positions in Iraq and Syria and has sent soldiers to help train members of the Iraqi national army.

That is nearly double the price of his previous most expensive work, bought by the same person a year ago.
It has broken several other records including becoming the most expensive work by any US artist.
It is also the highest price fetched for any art by a black artist and the first piece created since 1980 to break the $100m mark.
The untitled work was done in oil stick, acrylic and spray paint, and depicts a face in the shape of a skull.
It was sold to Yusaku Maezawa, a 41-year-old Japanese fashion entrepreneur who plans to set up a museum in his home town of Chiba.
Bidding for the piece during the auction at Sotheby's lasted 10 tense minutes. Cheers and applause erupted in the room when the work was sold to Mr Maezawa by telephone.
He later posted on Instagram that the painting made him feel "so much excitement and gratitude for my love of art", a feeling he wished to share with "as many people as possible".
Mr Maezawa last year set the previous record for a Basquiat piece, when he paid $57.3m for a painting of a horned devil.
Basquiat, a native New Yorker, died in 1988 of a heroin overdose aged 27. He had been an artist for just seven years.
Most of his works depict the problems faced by African Americans in the US, reports the BBC's Laura Bicker in Washington.
Once a graffiti rebel from Brooklyn who sold drawings for $50, he is now in the same league as Pablo Picasso and Francis Bacon, she says - part of a rare group of artists whose work has sold for more than $100m at auction.
"Breaking $100m for a work which is that recent is definitely extraordinary," said Gregoire Billault, head of contemporary art at Sotheby's.
"I think it just speaks about the talent of this guy. It's just pure emotion. He's bringing something never seen before."
Australia's top spy has said there is no evidence of large-scale militant attacks planned against the country.
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A painting by the late artist Jean-Michel Basquiat has sold at auction in New York for $110.5m (Â£85.4m).