Mr Rockliff also backed constitutionally enshrining an Indigenous voice to the Australian parliament, a key reform promised by the new federal Labor government.
"Australia Day, it is a national conversation of course and one that I am increasingly concerned ... is becoming increasingly divisive," he told state parliament on Wednesday.
"By nature I am not a divisive person.
"Bringing people together, Aboriginal people in Tasmania, all Tasmanians, to unite and celebrate Australia Day (on) a day we can all unite is a clear objective of mine."
Mr Rockliff, a long-term deputy who became premier in April when Peter Gutwein unexpectedly quit politics, was responding to a question from Labor MP David O'Byrne about whether he backed moving Australia Day.
During his time in the state's top job, Mr Gutwein said he supported a national conversation about changing the day and that reverting to a weekend in January, and not a set date, would be a sensible compromise.
"You outlined the previous premier's view on this particular matter and I support that view," Mr Rockliff said.
"You mentioned the ... last weekend in January … the previous premier's view on that, I support. I was deputy when he made that statement."
Aboriginal Land Council of Tasmania manager Rebecca Digney said it was incredibly heartening to hear the premier recognise Australia Day as divisive.
"For a very long time, Palawa/Pakana people have taken to the streets each Australia Day to tell the broader public what the day represents to us," she said.
She said there was no reason the island state could not change the date, citing moves by several Tasmanian councils in recent years to shelve Australia Day celebrations on January 26.
Mr Rockliff attended a Reconciliation Tasmania breakfast on Wednesday which included a speech from Uluru Statement from the Heart signatory Thomas Mayor.
The premier said he supported Mr Mayor's "very clear argument" with respect to changes to the constitution to enshrine an Indigenous voice to parliament.
Mr Rockliff said he was deeply committed to setting up an Aboriginal-led treaty and truth-telling pathway, a process started by Mr Gutwein.
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