The Prime Minister is under mounting pressure to make the Supreme Court appointment process more transparent and less ideological, after revelations that four of the government's six candidates were from a court that was ultimately ruled ineligible.

Opposition parties are accusing the Conservative government of distorting the process, while the Premier of Quebec voiced strong objections as well. The Opposition also demanded that the vacancy on the country's highest court – entering its 10th month – be filled by the end of June, and called on the government to apologize to Supreme Court Chief Justice Beverley McLachlin for accusing her of improper conduct.

"Conservatives rigged the process to make sure that at least one of the three final candidates would be from the Federal Court. Why?" New Democratic Party Leader Thomas Mulcair asked Prime Minister Stephen Harper in the Commons on Monday, after The Globe and Mail revealed the short list at the centre of the unprecedented rift between the Prime Minister and the Chief Justice.

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In Quebec, Premier Philippe Couillard said Ottawa's way of proceeding was insulting to the province's legal community and demanded changes.

"This is not the way we want the process to be conducted," Mr. Couillard said. "Having a say over who is chosen has always been part of Quebec's traditional demands." Justice Minister Stéphanie Vallée said Ottawa appears open to listening to Quebec's views on the next appointment.

Court watchers are angered at the long time it is taking to fill the job left vacant last August by the retirement of Justice Morris Fish. "It's bush league. There's no reason, just 'we don't give a shit.' I think that's disrespectful," political scientist Peter Russell of the University of Toronto said in an interview.

Justice Minister Peter MacKay said in the Commons that the vacancy would be filled "very soon." Neither he nor Mr. Harper apologized. Neither of them challenged opposition members when they cited the number of Federal Court judges on the candidate list.

Mr. Harper told Mr. Mulcair the government believed judges from the Federal Court were in fact eligible. In March, the Supreme Court ruled 6-1 that Mr. Harper's latest appointee, Justice Marc Nadon of the Federal Court of Appeal, was ineligible because he lacked current Quebec qualifications, as set out in the Supreme Court Act.

"The reason Federal Court judges were considered for this appointment is that Federal Court judges have always been considered eligible, up to and including the appointment of Justice [Richard] Wagner," Mr. Harper said. No Federal Court judge has ever held one of the three seats set aside for Quebec on the Supreme Court. The PM chose Justice Wagner from the Quebec Court of Appeal in 2012, but a source told The Globe that two candidates were from the Federal Court.

Liberal MP Stéphane Dion said the government had been looking for a judge most aligned with a conservative ideology, and became frustrated when the court rejected Justice Nadon and then "shamefully attacked" the Chief Justice, in statements in which the Prime Minister and Justice Minister said she had tried to have an inappropriate conversation about a case. (The Globe story showed that she had been raising the potential ineligibility of four candidates of six, not just one as previously believed.)

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On the short list of three judges from which Mr. Harper chose Justice Nadon, just one judge is eligible: Justice Marie-France Bich of the Quebec Court of Appeal. Mr. MacKay did not indicate whether he would stick with the original list.

Prof. Russell said the failure to fill the vacancy in a timely way could be seen as a constitutional violation, because the Supreme Court has ruled that its composition is protected by the constitution. But the court cannot launch that case on its own; someone would have to bring such a case to Federal Court, he said.

With a report from Rhéal Seguin in Quebec City