Peters also expressed concern.
"The New Zealand Government is very concerned with the violence and humanitarian crisis in Rakhine State, and we continue to urge the Myanmar government to do all it can to safeguard those affected," Peters said.
Of the additional funding, $500,000 will go to the World Food Programme and $1m to the UN Population Fund (UNFPA), for life-saving food, nutrition, protection and healthcare assistance among displaced families in Cox's Bazar District, Bangladesh.
The New Zealand money would also help address the sexual and reproductive health needs of women and girls, and the needs of survivors of sexual violence. An estimated 58,000 displaced women are pregnant and require healthcare to ensure safe pregnancy, labour and delivery.
The Government also pledged to match dollar for dollar up to $1m for funds raised by New Zealand NGOs for this crisis.
Foreign Affairs Under-Secretary Fletcher Tabuteau will head to Myanmar this weekend to attend the 13th Asia-Europe Meeting (ASEM). It will be chaired by Aung San Suu Kyi, who sat next to Prime Minister Jacinda Ardern at a gala dinner during Apec.
Among issues to be discussed will be North Korea, nuclear non-proliferation, economic development, and connectivity.
"I look forward to the meeting with the Asia and European representatives from two regions, which are of great importance to New Zealand," Tabuteau said.
"I will also take the opportunity to discuss the crisis in northern Rakhine with the Myanmar authorities."
Early this afternoon, Peters said he was not in a position to reveal the substance of his meetings with Tillerson, but Ardern said it would be revealed in due course.