The Government will give an extra $2.5 million for the Rohingya refugee crisis in Myanmar, which has seen more than 600,000 ethnic Rohingya flee their homes and seek refuge in Bangladesh.

Foreign Minister Winston Peters made the announcement this afternoon, bringing the total amount of New Zealand money to help those caught up in the crisis to $4m.

The Herald understands that the additional funding is the reason US Secretary of State Rex Tillerson, who is Myanmar today, sought meetings with Peters on the sidelines of the Apec meeting in Vietnam this week.

Tillerson met with Myanmar leader Aung San Suu Kyi today and called for an independent investigation into Myanmar's treatment of the Rohingya Muslim people.

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He expressed concern, but stopped short of calling for sanctions on Myanmar, or suggesting that it "looks like ethnic cleansing", as British Prime Minister Theresa May did.

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.