Conservative senator Concetta Fierravanti-Wells says polling indicating support for marriage equality among Australians does not encompass the whole community.
Speaking at the National Press Club on Wednesday, the assistant minister for multicultural affairs said traditional marriages and family values were important to Australia's culturally diverse communities.
"Same-sex marriage is not a priority but if it is made a priority, it would raise strong opposition to the faith of many Australians, including, especially our migrant communities who consider marriage a bedrock institution," she said.
"Hence, I argued strongly that a Coalition policy that directly supports same-sex marriage could place under threat some of our most marginal seats which have disproportionately high religious and migrant communities."
Fierravanti-Wells added that she believed a "silent conservative majority" would prevail in a number of marginal seats with high culturally and linguistically diverse populations.
Polling on marriage equality fails to include culturally diverse communities and older people, Fierravanti-Wells said.
Polling has consistently shown strong support for marriage equality, with results mostly ranging from 60% to 70% of Australians in favour.
"The proponents of same-sex marriage refer to polling," Fierravanti-Wells said.
"I would doubt that such polling captures the view of culturally diverse members, especially the older ones likely to take heed of the advocacy of their religious leaders rather than their local politician or answer a phone call from a pollster."
Religious leaders have a large role to play in the debate, she added.
Current government policy on same-sex marriage is to hold a national plebiscite on the issue after the 2016 election.