Communal violence has torn through Rakhine state since August 25, leaving hundreds dead and driving more than 410,000 of the Rohingya minority from Myanmar into Bangladesh.
Suu Kyi, a Nobel laureate, has been decried for failing to speak up publicly for the stateless Rohingya or urge restraint from the military.
"Hate and fear are the main scourges of our world," she said.
"We don't want Myanmar to be a nation divided by religious beliefs or ethnicity... We all have the right to our diverse identities."
While expressing her sorrow for "all" groups displaced by violence, she said her country stood ready "at any time" to take back refugees subject to a "verification" process.
It was not immediately clear how many of the estimated 410,000 Rohingya who have fled Myanmar would qualify to return.
Myanmar's army has previously it will not take back people linked with "terrorists" -- suggesting many came from the hundreds of Rohingya villages that have subsequently been burnt to the ground.
Inside Myanmar, supporters say the 72-year-old lacks the power to rein in the army, with whom she is in a delicate power-sharing arrangement.
The UN has accused Myanmar's army of "ethnic cleansing" over a campaign of alleged murder and arson that has left scores of Rohingya villages in ashes.
Since then just under half of Rakhine's Rohingya population has poured into Bangladesh, where they now languish in one of the world's largest refugee camps.
A further 30,000 ethnic Rakhine Buddhists as well as Hindus have also been displaced -- apparent targets of the August 25 attacks by the Arakan Rohingya Salvation Army (ARSA) militant group.
Suu Kyi skipped this week's UN General Assembly in New York to manage the crisis at home and deliver her televised address -- the biggest yet of her time in office.
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