Canada and the United States are in talks about how they can intensify pressure on Myanmar’s powerful military leadership for its role in ethnic cleansing against Rohingya Muslims, amid reports that 480,000 members of the minority group have fled violence in the Southeast Asian country.

Foreign Affairs Minister Chrystia Freeland said she spoke with U.S. Secretary of State Rex Tillerson on Monday night about ways to step up pressure on Myanmar’s military leadership, but did not mention any specific plans. Speaking to the House of Commons during an emergency debate on the violence facing Rohingya, Ms. Freeland underlined the importance of holding Myanmar’s military to account.

“It is very important that the military in Myanmar understand that the world is aware of the military’s role in this ethnic cleansing and that we will not stand for it,” said Ms. Freeland, who took time away from NAFTA negotiations in Ottawa to address the House of Commons Tuesday night.

Myanmar’s de facto leader Aung San Suu Kyi does not have the authority to direct security matters, as the military retained significant power under Myanmar’s 2008 constitution. However, the Nobel laureate and honorary Canadian citizen has still faced sharp international criticism for her inaction on the recent Rohingya crisis.

In a Sept. 18 letter to Ms. Suu Kyi, Prime Minister Justin Trudeau said the responsibility for resolving the crisis falls “squarely upon” Ms. Suu Kyi and military commander-in-chief Min Aung Hlaing.

Conservative MP Garnett Genuis, who requested the emergency debate, asked Ms. Freeland if she had spoken with General Hlaing directly. Ms. Freeland said Canada has put pressure “directly to the military leadership,” but did not indicate if she spoke with Gen. Hlaing.

Human Rights Watch said on Tuesday that Myanmar is committing crimes against humanity in its massacre of villagers and mass arson in Rakhine state, where 480,000 Rohingya have been forced to flee to neighbouring Bangladesh over the past month. A Myanmar government spokesman said there was no evidence to support that claim.

Ms. Freeland said Canada has three goals for the continuing Rohingya crisis: to end the ethnic cleansing; to ensure that humanitarian assistance can reach the minority group; and to work with international allies to allow Rohingya to return to Rakhine and live free of persecution.

The current outbreak of violence began at the end of August, after Rohingya insurgents attacked dozens of police posts and an army base in Rakhine. Myanmar’s military responded by killing hundreds of people, triggering a massive exodus of Rohingya villagers. UN Secretary-General Antonio Guterres has described the situation as ethnic cleansing.

Heading into the United Nations General Assembly last week, the Liberal government said it was planning to focus on the plight of Rohingya, among other current international issues. While Mr. Trudeau and his cabinet colleagues raised the situation of Rohingya during bilateral meetings on the sidelines of the UN, his speech made no mention of the matter.

“The Prime Minister should have raised this issue during his speech to the UN General Assembly last week,” Mr. Genuis said.

Ms. Suu Kyi did not attend the UN General Assembly, staying in Myanmar to deliver her first national address since the massive Rohingya exodus. In her speech, she condemned rights abuses in Rakhine and said violators would be punished. While Western diplomats and aid officials welcomed the tone of her speech, some doubted if she had done enough to deflect international criticism.

NDP MP David Christopherson, who has met Ms. Suu Kyi, told the House of Commons that she is the best hope for Myanmar, while acknowledging her lack of power over the military.

“We’re going to make sure that the world knows that we’re holding the military to account because we understand the difficulty that [Ms. Suu Kyi] has and my heart breaks for that situation.”