Canada is facing mounting pressure from senators, and members of the civil society and rights groups from across the country to take more international action in holding Myanmar accountable for the Rohingya genocide, reports The Canadian Press.

Thirty-four senators -- a third of the Senate -- and more than 100 human rights organisations and advocates sent a joint letter to Canadian Foreign Minister Chrystia Freeland this week urging Canada to initiate proceedings before the International Court of Justice over the breaching of the United Nations convention against genocide.

In September 2018, Canada became the first country in the world to officially recognise the violence against the Rohingya by Myanmar's security forces as 'genocide'. Canada also stripped Myanmar's de facto leader Aung Sun Suu Kyi of her honorary Canadian citizenship for her inaction over the issue.

But branding the situation a genocide carries with it a legal and international obligation to intervene, potentially with force, which is why the push is now on to see Canada take this next step, the joint letter states.

"As concerned parliamentarians and members of the civil society, we strongly believe that those responsible for the genocide against the Rohingya must be held to account by the international community.

"We firmly believe that Canada is in a position to exercise strong and effective global leadership in response to the genocide by pursing this matter before the International Court of Justice," it says.

Similar letters have been sent to Chrystia Freeland and Justice Minister David Lametti in recent weeks, including one from an all-party group of MPs, which also called for Canada to take international legal action.

In addition, Toronto and Montreal city councils have passed unanimous motions and several other Canadian mayors and other rights organisations have sent their own letters to Freeland urging Canada to seek justice for the atrocities perpetrated against the Rohingya in Myanmar.

Independent UN investigators last year demanded an investigation into the allegations against the Myanmar military of a genocide that forced over 741,000 Rohingya flee to Bangladesh.

In a statement on Thursday, Freeland's Deputy Press Secretary Marie-Pier Baril said the government believes those responsible for the atrocities against Rohingya Muslims must face punishment, noting that Canada has sanctioned its key military commanders.

But rather than initiating the process independently, Canada has called on the UN Security Council to refer the situation faced by the Rohingyas to the International Criminal Court.

"Canada will continue to lead international efforts to support the Rohingya's basic needs, to exert pressure on the Myanmar government and to bring justice to the Rohingya for all they have suffered," Baril said.

Fareed Khan, spokesperson for the Rohingya Human Rights Network, stressed the need for more urgent action to help the hundreds of thousands who have fled the country and the hundreds of thousands more who remain trapped in Myanmar, facing ongoing rape, torture and death.

"As Canadians, as human beings, it's our moral responsibility to act, to lift the Rohingya out of the despair and hopelessness that many of them feel because of what they have endured," Khan said during a recent press conference in Ottawa.