Migrants need to be able to speak English to participate in Australia's national life, Prime Minister Tony Abbott says.
But he stopped short of echoing government Senator Concetta Fierravanti-Wells' call for migrants to make English their main language.
The senator, who is the parliamentary secretary for social services, told Fairfax people had a "personal obligation" to learn English.
She recounted starting kindergarten in Wollongong without being able to speak English and said that she had learned to speak it within three months.
"Retaining a knowledge of one's mother tongue is important but not at the expense of learning English," she told Fairfax.
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Mr Abbott said Senator Fierravanti-Wells was explaining her family's experiences with the importance of language.
"Yes, it is important for people to fully participate in Australia that they master our national language," he told reporters at the national citizenship ceremony in Canberra on Sunday.
"But as you can all see, there are lots of people who become Australian. From all sorts of cultures, all sorts of backgrounds.
"We don't have any expectations on anyone except that they join the team and that they become Australian in their own way and at their own pace."
Opposition Leader Bill Shorten used his Australia Day speech, at a citizenship ceremony in Melbourne, to praise the contributions migrants have made during the course of the nation's history.
"This is the true Australian tradition," he said.
"Not just a British one, or an indigenous one but a tradition woven from all the countries, all the peoples, all the cultures of the world."
Sunday marks the 65th anniversary of the Nationality and Citizenship Act, which created the status of Australian citizen.
Mr Shorten told reporters in Melbourne that Australia Day was not a day for "simplistic stereotyping" of immigrants.
"In my experience, there's not a single immigrant that comes to Australia that is not hungry to succeed, to make their family do better, but also to make their new adopted homeland be a better country than it already is," he said.
