Mr Turnbull said he recognized the history of European settlement in Australia had been "complex and tragic for Indigenous Australians", but indicated that changing the national day was not the right way to redress this.
"A free country debates its history – it does not deny it. It builds new monuments as it preserves old ones, writes new books, not burn old ones."
"In a world too often riven with discord and violence, we have so much to celebrate here in Australia."
His video message came as Greens leader Richard Di Natale announced his party would organise a major political campaign focused on abandoning January 26 as the official date of Australia Day.
"We need to acknowledge that there are people who see January 26 as a day that represents pain and suffering, the ongoing effect of which can still be felt today," Mr Di Natale said.
"We want to choose a day that brings the nation together."
January 26 marks the date the First Fleet landed in Sydney Cove in 1788 and the beginning of British colonisation in Australia.
Nationals leader Barnaby Joyce also criticised the Greens' plans.
"They dwell in the philosophical, we build the things that actually make our nation stronger," Mr Joyce said.
"I don't care, wherever you've come from, you've come to this nation and this nation is now your home."
"We have a day to celebrate it, and it's called Australia Day. I look forward to celebrating it this year."