Australia's Prime Minister Tony Abbott is under pressure to increase the country's total refugee intake.
Mr Abbott has said more Syrian asylum seekers would be let in but has stopped short of boosting total refugee numbers.
But members of his own party, including several state premiers, have called for more to be done for refugees.
Assistant Treasurer Josh Frydenberg on Monday called for temporary housing of Syrian and Iraqi asylum seekers.
Mr Frydenberg said there was a good case for a Kosovo-type solution that would see Syrian and Iraqi refugees housed in Australia, then returned home once the countries were safe.
The Liberal Premier of Australia's most populous state, New South Wales, Mike Baird, on Saturday challenged Mr Abbott to do more than just stopping refugees making their way to Australia by boat.
Reacting to a photo of a Syrian child refugee recently found drowned on a Turkish beach, Mr Baird said he felt "sick with overwhelming sorrow" about the situation.
Mr Baird, a close colleague of Mr Abbott's, said it was a great thing that Australia was no longer seeing children drowning at sea after trying to get to Australia by boat with their families.
"But stopping the boats can't be where this ends ... I believe we should do even more. And we should do it now," he said, adding that he would talk to the Federal government about what could be done.
Australia detains any migrants trying to reach its shores by boat, and takes them to offshore processing centres to be resettled elsewhere.
Last week, the New York Times described the policy as "brutal".
'Open door'The lightly-populated island state of Tasmania has also said it would accept an extra 500 refugees, with Liberal Premier Will Hodgman declaring "our door's open".
Australia has accepted about 4,500 people fleeing Syria's conflict, under its current commitment of 13,750 refugees for 2015.
Mr Abbott has claimed Australia is "already the most generous country in the world on a per capita basis when it comes to dealing with refugees through the UNHCR".
Several organisations have challenged that claim.
'Awful imagery'During a press conference on Sunday, the Prime Minister spoke of how horrified he was by the image of the drowned Syrian boy.
"No parent could fail to be moved by what we saw," he said.
"I have asked the Immigration Minister Peter Dutton to go urgently to Geneva to talk to the UN High Commissioner for Refugees on what more Australia can do to assist on the migration crisis that is being driven by the problems in the Middle East," he said.
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