Metro Manila (CNN Philippines, May 17) — A week after Chief Justice Maria Lourdes Sereno was ousted, President Rodrigo Duterte bared the qualities of the next top magistrate he is set to appoint.

"Gusto ko 'yung bilib ang tao sa integrity niya [I want someone with integrity]. Of course it could not be a politician, lalo na hindi babae [especially not a woman]," Duterte told reporters in Malacañang Tuesday.

However, the former Chief Justice disapproved of Duterte's preferences.

"You know the Constitution installs the equality of the sexes. So mukhang hindi niya yata mahal ang Constitution," she said in a forum Wednesday. "Ang mga kababaihan ay kailangang bigyan ng oportunidad."

Presidential Spokesperson Harry Roque was quick to defend the President, saying that what he heard was a question regarding the next Ombudsman.

"Ang narinig ko lang is, tatanungin niya 'yung mga taga-Ombudsman, pero hindi 'yung babae, hindi si Chief Justice," he told CNN Philippines.

[Translation: What I heard is he'll ask those in the Ombudsman, but not the woman, not the Chief Justice.]

However, Roque said he will check the President's statement again. He added the President has no choice but to select from those shortlisted by the Judicial and Bar Council (JBC).

"So it's not as if the President can block anyone out from thin air. His choices are limited and he can't even say who his preferences are at this point because he does not know who will be shortlisted," he said.

In a later briefing in Malacañang, Roque clarified that the President does not discriminate against women.

"Sa aking pagkakaalam po wala naman pong diskriminasyon against sa kababaihan. Kahit sino po pwedeng ma-appoint sa ating gobyerno," Roque said.

[Translation: As far as I know there's no discrimination against women. Everyone can be appointed to government.]

Sereno was removed from her post on May 11 through a Supreme Court decision which invalidates her appointment as Chief Justice, after failing to meet the requirement of submitting her Statements of Assets, Liabilities and Net Worth (SALNs) from 2002, to 2006. The JBC was ordered to begin the vetting of Sereno's successor.

'Reeking of misogyny'

Former Chief Justice Hilario Davide said Sereno's womanhood may have played a factor in her ouster.

"That could be the reason why he is very, very much interested in having our beloved Chief Justice ousted," he said Wednesday.

Meanwhile, the advocacy group #EveryWoman said Duterte's statement "reeks of his now well-known misogyny."

"From the way he sexually harasses the last few women in his official family to this statement that implies that women cannot really have political integrity nor brilliance, Duterte highlights the most disgusting aspects of Philippine machismo," it said in a statement Thursday.

The group also said Duterte should keep his hands off Sereno.

"There is someone here who is patently unfit for office. And it's a he, not a she," the group said.

Duterte in April called Sereno his enemy, after the former Chief Justice questioned his involvement in the quo warranto petition filed by Solicitor General Jose Calida.

The President reiterated he did not interfere in Sereno's ouster.

"I challenge everybody and anybody magturo ng isang congresswoman, senador, o justice ng Supreme Court na nilapitan o maski abogado lang," he said. "Hindi nga ako nakikialam eh."

[Translation: I challenge everybody and anybody to point a congresswoman, senator, or justice of the Supreme Court that we talked to, or even just a lawyer. I did not interfere.]

Duterte is also set to appoint a new Ombudsman, as Ombudsman Conchita Carpio Morales will retire in July. He said he will consult Ombudsman officials and employees before choosing from the JBC shortlist.

Among those in the list is Labor Secretary Silvestre Bello.

Bello keen on taking Ombudsman post

Morales and Duterte have been at odds after the former inhibited against her office probe into the unexplained wealth of the first family.

In October 2017, Duterte said impeachment proceedings against the two women were underway, after accusing them of corruption.

Related: Impeachment proceedings vs. Sereno, Morales underway