One million Australians travel to Indonesia every year.
Prime Minister Malcolm Turnbull condemned the attacks and expressed his condolences.
"Our heart goes out to all of the victims of those attacks and the people of Indonesia know that they have our utmost solidarity in the battle against terrorism," Mr Turnbull told reporters in Sydney.
"It almost beggar's belief; the brutality, the barbarity, the inhumanity, the blasphemy of these terrorists."
He has written to Indonesian President Joko Widodo to express heartfelt sympathy.
Foreign Minister Julie Bishop said Australia will continue to work closely with the Indonesian government and law enforcement agencies to help to foil future terror plots.
"We condemn these cowardly attacks" she said.
Home Affairs Minister Peter Dutton said Australia stands united with Indonesia.
"This threat is not going away and Australia stands absolutely united with a very, very crucial friend in Indonesia to make sure we can work with the president and ... the Indonesian government to keep their people safe," Mr Dutton told reporters in Canberra on Monday.
"Evil has prevailed in recent hours."
He said the fact women and children were involved in the church bombings was particularly "egregious".
Opposition Leader Bill Shorten and Labor's foreign affairs spokeswoman Penny Wong said the attacks had no basis in religion and were an affront to peace-loving people of all faiths.
"It is particularly concerning to hear reports of the attacks being carried out by a single family, which murdered its own children," they said in a joint statement.
Former prime minister Kevin Rudd said the incidents were a "sobering reminder" of the new danger posed by Islamic State fighters returning from Syria and Iraq.
"Significant threat to Australians and westerners in SEA (South East Asia) region," he tweeted.
Last year, the Philippines scrambled to quash a five-month IS insurgency in Marawi.
Australia provided surveillance aircraft and has been training Filippino troops in urban combat.
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