Malcolm Turnbull accepts there are some people who staunchly oppose the date of Australia Day, but insists the overall number is "not many".
"You know, the overwhelming majority of Australians are celebrating Australia Day like we all are here today," he said on the shores of Lake Burley Griffin in Canberra on Friday.
"They are just in love with our nation, with our story, with our people, with our success - the most successful multicultural society in the world."
As disagreement intensifies over shifting the national day from the January 26 anniversary of the First Fleet's arrival in 1788, thousands are attending "Invasion Day" marches around the country.
Far right groups are also preparing to rally in support of retaining the date.
The prime minister said Australians should focus instead on recognising First Australians and being honest, open and truthful about the country's past.
While Australia's history was overwhelmingly "a bright story of success" the impact of European settlement on Aboriginal and Torres Strait Islanders was tragic.
"There are many wrongs that were done in the past, which we seek to right today," Mr Turnbull said.
"We should be focusing on closing the gap, on health, on education, telling our story honestly, but above all, remembering that this is a story of enormous achievement."
Asked about the Australian flag, Mr Turnbull said he could not see it changing, regardless of whether the country ever becomes a republic.
He said young people did not pick apart the flag to scrutinise the UK's Union Jack.
"They look at it as one Australian symbol - that's the one they have on their backpacks when they're travelling overseas, that's the flag that our soldiers have on their shoulder patches, that is our flag," Mr Turnbull said.
"So, I think the Australian flag will be flying over Parliament House long after all of us have shuffled off the stage of history."