Islamic State has claimed responsibility for Tunisia and Kuwait, and an Islamist flag was displayed at the French site.
Mr Abbott said Australia was committed to tackling the threat of global terrorism, and was making "a strong contribution at home and working closely with our partners abroad".
Foreign Minister Julie Bishop earlier said she would contact her counterparts in France, Tunisia and Kuwait to express Australia's support.
Labor has also condemned the attacks and said it would do all it could to support the federal government.
"These were attacks aimed at the innocent. Acts of hatred, designed to provoke fear," Opposition Leader Bill Shorten and deputy leader Tanya Plibersek said in a joint statement on Saturday.
Mr Abbott said Australians should remain vigilant, and urged anyone who sees or hears something that they feel is not right to contact the National Security Hotline on 1800 123 400.
"Our security agencies are assessing the situation for any implications for us but there is no information to suggest a higher threat to Australia as a result of these latest atrocities," he said.
Treasurer Joe Hockey said the national security committee would meet on Saturday and the attacks were a reminder of the risk of terrorist attacks anywhere in the world.
"That's why we're working so hard to put all the resources in that we can to defeat these evil bastards at their source," told reporters in Melbourne on the sidelines of the Liberal Party federal council.
No Australians are believed to have been caught up in the attacks, but those worried about family or friends should contact the Department of Foreign Affairs and Trade.
Meanwhile, the Northern Territory News has reported that a 16-year-old Darwin teenager is facing terrorism charges after he was allegedly found with a list of people he wanted to behead.
