Foreign Minister Julie Bishop is working with several departments to see how the government can respond to the plight of baby Gammy.
A West Australian couple have been accused of taking his twin sister and leaving the boy, who has Down syndrome, behind in Thailand with their surrogate.
Ms Bishop said she has asked the Department of Foreign Affairs and Trade to work with the Department of Immigration and the Attorney-General's department to consider the government's response.
"We are looking at it from every angle," she told reporters in Canberra on Tuesday.
Prime Minister Tony Abbott agreed there were no easy answers.
"The one shining light to come from this most unfortunate, deeply regrettable situation is there appears to have been an absolute outpouring of generosity towards baby Gammy and his mother," Mr Abbott told reporters.
"That's the one thing I would like to say redeeming this otherwise terribly, terribly unfortunate situation."
Opposition Leader Bill Shorten said what had happened in the baby Gammy case in the past few days was devastating and called for the complex laws governing overseas surrogacy to be made clearer.
"Australians who want to be loving parents, I can understand that they are most motivated to have that most amazing experience to be a parent, but we have to balance that and make sure that when it engages in jurisdictions beyond our own the rules are really clear," Mr Shorten told reporters.