The Islamic Women's Welfare Association also says Muslims prefer to live close to their own people and Australia should consider how to "facilitate the purchase of homes for new migrants".
In a submission to a federal multicultural inquiry, the association has urged the Government to give tax deductions to newly arrived migrants so they can visit relatives in their homelands.
"Migrants face a lot of sacrifices such as having to travel long distances to visit relatives, spending on communication costs, missing out on some events occurring in native countries etc," the submission said.
"This loss should be compensated by the Government in one way or the other to retain migrants in their country of adoption."
Victorian Muslim and president of the Australian Council of Bosnian Organisations Senada Softic-Telalovic said while some help might be justified for needy refugees who had to go overseas to settle their affairs, she didn't support travel compensation for all newcomers.
That type of argument will bring out further outrage from those who are so anti-migrant and so anti-multiculturalism," she said. Ms Softic-Telalovic said that Australia was seen as an ideal migration destination and new arrivals shouldn't take the country for granted.
"Migrants and refugees who come out now are in a significantly better position and you could say a more privileged position than those who came out in the 1970s," she said.
Victorian Multicultural and Citizenship Minister Nick Kotsiras said tax breaks for migrant trips abroad was a ridiculous idea.
"We are all equal and no one should get special privileges," he said.
The Islamic welfare association is based in Lakemba, Sydney, which has one of the highest Muslim populations in Australia.