A group of Canadian lawyers and law professors has asked the International Commission of Jurists to launch an inquiry into the prime minister's remarks.
They allege that Harper attacked the independence of the high court and that his comments could be construed as a form of intimidation.
The controversy erupted shortly after the Supreme Court nixed the appointment of Marc Nadon to the top court's bench.
The court found Nadon ineligible to sit as one of three Quebec justices on the Supreme Court because he came from the Federal Court of Appeal.
The Supreme Court Act specifies that Quebec judges must come from either the province's Court of Appeal or Superior Court, or have at least 10 years standing at the Quebec bar.
Harper went on to accuse Supreme Court Chief Justice Beverley McLachlin of trying to make an "inadvisable and inappropriate'' phone call to warn him there might be an eligibility problem with Nadon's appointment.
On Wednesday, Mulcair replied in the affirmative when asked whether Harper's comments are besmirching Canada's reputation internationally.
"Yes," he said.
"Once again Stephen Harper is staining Canada's reputation abroad. This time it's with his inability to respect one of the basic rules of our democracy — which is the respect of the separation of powers.
"So he should apologize but we know Stephen Harper. He thinks he's always right."
Liberal Leader Justin Trudeau also weighed in, saying Canada has lost lustre on the world stage since the Tories took power in the mid-2000s.
Part of the International Commission of Jurists' mandate is to protect the independence of the judiciary.
The Geneva-based group has not yet indicated whether it will investigate.
Its website indicates that most of its investigators are not active at all in North America and are concentrated mainly in Africa, Asia and Russia.
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