Mulcair told CTV News that MacKay has demonstrated a "bizarre attitude" with his recent remarks about the dearth of female judges in Canada and emails to staffers that some have derided as sexist.
The NDP leader says MacKay doesn't understand his obligation to uphold equality rights under the Charter of Rights and Freedoms.
"I know that Stephen Harper doesn't embarrass easily with regard to the behaviour of his ministers but frankly, this time around, to have a justice minister saying those types of things about women becoming judges, women's role in society, it shows that he is completely out of phase with the Charter of Rights," he said.
"I think that Mr. Harper's going to have to move in and either explain things to Peter MacKay or replace him with somebody who understands the Charter of Rights and the fact that this is actually the 21st century."
Mulcair said he is "reticent" to call for ministers to resign but says the recent controversy, combined with the botched attempt to appoint Marc Nadon to the Supreme Court, shows MacKay is "not very good at his job."
The NDP leader suggested the minister has shown twice in two weeks that he has a "world view" that clashes with the times.
"He has a completely different view of the role of men and women in our society," Mulcair said. "And again, this might have been appropriate 100 years ago but in the 21st century, it doesn't reflect reality."
MacKay has been in hot water since The Toronto Star reported he told members of the Ontario Bar Association earlier this month that women don't apply to be judges because they fear the job will take them away from their children.
Then, The Canadian Press revealed that his emails to staff on Mother's Day and Father's Day raised eyebrows because they were very different in tone. The moms were lauded for doing things like changing diapers, the dads for shaping the next generation of leaders.
MacKay told The National Post that the emails were actually written by a female staffer in his department but that only led to accusations he was ducking controversy.
On Thursday, MacKay's wife Nazanin Afshin-Jam wrote an open letter to The Globe and Mail defending her husband and criticizing both journalists and the lawyers who she said ran to the "anti-Conservative media with hearsay."
Her letter was actually in response to an earlier piece from a Globe columnist Leah McLaren, who called on Afshin-Jam to "shape and mould" her husband’s mind.
Afshin-Jam said her husband's remarks have been misrepresented and organizers from the OBA meeting have turned down MacKay's request to release the audio recording of his comments to lay the matter to rest.
The justice minister was tight-lipped about the controversy when pressed by reporters Friday.
"I think enough has been said about what I didn't say," he said.
Meanwhile, some are wondering if a mountain is being made out of a molehill.
Long-time Tory MP Laurie Hawn has called the emails controversy "utter nonsense" and Harper has said MacKay's staff memos weren't sexist.
National Post columnist Chris Selley wrote Friday that while MacKay made a "royal hash" with his reported remarks about female judges, the media pile-on about the emails has been embarrassing.
"All Peter MacKay did was ask a staffer to compose some nice things about the mothers and fathers in his employ, and he's been pelted with cream pies ever since," he wrote.
And Selley doesn't think much of Mulcair's calls for the justice minister to resign.
Well, we have officially lost our minds (again). Mulcair calls for MacKay to resign over emails http://t.co/xt5F8BwFA3— Chris Selley (@cselley) June 27, 2014
Do you think Mulcair is overreacting in calling for MacKay to either step down or be fired by Harper? Tell us in the comments.
With files from The Canadian Press
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