The United Nations and rights groups say some 700,000 people, most of them Rohingya, have fled from Myanmar into Bangladesh since August last year when Rohingya militant attacks on the security forces sparked a military crackdown.
The United Nations and several Western countries have said the Myanmar action constitutes ethnic cleansing but Myanmar rejects that. It says its security forces have been conducting legitimate operations against "terrorists".
Drawing the ire of officials in Myanmar, Duterte then expressed sympathy for the Rohingya and offered to help.
"I really pity the people there," Duterte said. "I'm willing to accept refugees. Rohingyas, yes. I will help but we should split them with Europe."
He also mentioned the inability of the international community to resolve problems in Myanmar.
"They can't even solve the Rohingya. That's what genocide is, if I may say so," Duterte said.
"He doesn’t know anything about Myanmar,” Zaw Htay told Reuters. "The usual behaviour of that person is to speak without restraint. That’s why he said that."
Duterte's comments were broadcast live on television and later included in a transcript of his speech, issued by his office.
Such a denunciation by a Southeast Asian leader of a neighbour is rare.
Both the Philippines and Myanmar are members of the Association of South East Asian Nations which has long upheld a convention of withholding criticism of fellow members.
Duterte did not refer by name to Myanmar leader Aung San Suu Kyi, who has been heavily criticised abroad for failing to stand up for the largely stateless Rohingya, only saying: "That woman, she is my friend."