Labor MP Matt Thistlethwaite has accused Prime Minister Tony Abbott of only taking action after members of his own party prodded him.
But Mr Abbott says a move by his Government to accept more Syrian refugees will not involve lifting Australia's overall humanitarian intake.
He says Australia has always done its part globally when it comes to refugees.
But World Vision Australia chief executive Tim Costello says the Australian government's generosity has dropped in recent years.
"We need to restore the old refugee humanitarian target, which just two years ago was 20,000 people. Under the Abbott Government, it was reduced to 13-and-a-half thousand. So, prioritising Syrians within the same limit is displacing other refugees, and I don't think that's very generous. It's like a powerful man taking money from a poor person to give it to an even poorer person and then saying, 'Aren't I generous?'"
By 2018, Australia's overall refugee intake will increase to 18,750, still below the 20,000 the Reverend Costello believes Australia should have now.
When that point was suggested to Mr Abbott in a later interview, the Prime Minister said the 20,000 figure was only briefly put in place by the former Labor government.
"I don't think we ever took that number, and let's never forget that, under the former Government, that number was filled by the people smugglers. We did, last year, take 4,500 people from Syria and Iraq, and we are looking at what more we can do."
During a meeting with the United Nations in Geneva, Immigration Minister Peter Dutton says, he will ask how the Australian government can help.
He says it could include financial support for people stuck in camps or what he calls "further assistance under the program to come onshore."
"Australians are prepared to do more, and the Australian Government is prepared to do more. We want to make sure that we can build on the numbers that we've already provided safe haven to."
Government frontbencher Josh Frydenberg says if Australia can do more, it should.
The Assistant Treasurer has suggested on Sky News that Australia should accept thousands more Syrian refugees as a one-off move.
"Firstly, we should focus on families and women and children. And we already do that, but I think we should be doing it in terms of our additional measures, given what we've seen now in Europe. And the second is maybe what John Howard did in 1999 with the Kosovars could be a bit of a guide for us. He took 4,000 at that time. Some of those went home, but he did provide a humanitarian response and shelter for people."
The safe-haven visas given to those refugees lasted three months.
Foreign Minister Julie Bishop says the Government is considering a similar scheme.
"I am also speaking with counterpart foreign ministers, some of our friends and allies, foreign ministers of countries in the region, to gauge what they will be doing and how we can work as part of an international effort."
South Australian premier Jay Weatherill says every state and territory should be doing its part to help people fleeing the Syrian war.
He has told the ABC up to 1,000 safe-haven visas should be issued for refugees to stay in his state.
Mr Weatherill says it does not need to disturb the existing humanitarian intake and it would be temporary.
He says he accepts there is a contradiction between rejecting people arriving in Australia by boat to discourage such journeys and accepting those who arrive by boat in Europe.
But he argues the moment calls for help without political complications.
"Where's the humanity in bombing a country -- and we're part of that, or being asked to be part of that -- but, at the same time, not offering a humane solution by giving them a safe place where they can come to because they're fleeing that sort of violence? It seems to me this is a pretty obvious human response to a human crisis."
Last week, New South Wales premier Mike Baird urged the Government to do more after a three-year-old Syrian boy's body washed up on the shores of Turkey.
Vigils are being held in support of the migrants in Sydney, Melbourne, Perth, Adelaide, Canberra and Brisbane.
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