Conservative leadership contender Peter MacKay said today he wants to march in Toronto's Pride parade.

MacKay said he's applied to the parade organizers for permission to participate. If he gets it, and if he wins the leadership contest — to be held the day before the parade, on June 27 — he'll be the first permanent federal Conservative leader to participate in this sort of LGBTQ rights celebration.

"Pride parades are important," MacKay said in a statement.

"We live in a world where sexual orientation and gender identity are still used by tyrants and bigots to belittle and oppress. In Canada we are lucky to have a society that has grown more tolerant, more accepting and more understanding, but there is still more work to be done."

MacKay has been more accepting of same-sex marriage rights than other Conservative politicians. In 2006, for example, he was one of only a handful of cabinet ministers to vote against his own government's resolution to restore the traditional definition of marriage.

MacKay anticipated criticism of his decision to march in Pride from some social conservatives in the party's ranks.

"The fact that some will condemn this statement speaks louder than any argument I could make about the importance for the next leader of the Conservative Party of Canada to follow in the footsteps of Rona Ambrose, and march in support of pride," MacKay said in his statement.

Outgoing Conservative Leader Andrew Scheer, a social conservative, did not participate in any of the country's many Pride parades during his time at the helm of the party. Scheer's decision to stay away from these events was a source of criticism during the last campaign, with some viewing his refusal as a sign that he did not fully embrace equal rights for sexual minorities in Canada.

"There's lots of different ways to show support to a community," Scheer said, when asked why he refused to attend.

Scheer backed a history-making government apology to LGBTQ public servants who were purged by the federal government because of their sexuality, and he embraced LGBTQ refugees fleeing countries like Iran, among other initiatives.

Rosemary Barton asks Conservative leader Andrew Scheer about how his views on LGBTQ rights have evolved. 2:10

Despite that show of support, Scheer was followed throughout the campaign by remarks he made in 2004 comparing same-sex marriage to a dog's tail. He also voted against protections for trans Canadians as recently as 2016.

MacKay himself said Scheer wasn't able to "deftly deal" with social issues like same-sex marriage and abortion when asked about them during the last election.

Talk of these issues "hung around Andrew Scheer's neck like a stinking albatross, quite frankly," MacKay said last fall.

O'Toole to skip Toronto Pride because of 'regrettable' stance on police

Erin O'Toole, an Ontario MP also running for the Conservative leadership, said Tuesday he would also be willing to march in Pride parades — but he would avoid the Toronto march because of its current "regrettable" policy of excluding uniformed police officers.

"In uniform, I stood up for the rights of all Canadians, and in Parliament, I have always voted for liberty and equality," O'Toole said in a statement, citing his time as a navigator in the Royal Canadian Air Force.

"When Toronto Pride becomes a truly inclusive event, I will march in that with my uniformed friends."

Toronto Pride has struggled with the question of how to include police.

Some members of the LGBTQ community, notably black and Indigenous activists, have said they feel uncomfortable with uniformed officers participating because of a history of police abuses against LGBTQ people. Others see the participation of police officers as a sign of progress that should be welcomed by Pride organizers.

MacKay and O'Toole have differed on trans rights in the past.

In 2013, O'Toole voted to support an NDP private member's bill to amend the Canadian Human Rights Act and the Criminal Code to include protections for "gender identity" and "gender expression." MacKay and many of his cabinet colleagues voted against the legislation — and it failed to pass. After the 2015 election, the Liberal government passed a similar measure. O'Toole didn't vote on that version of the bill.

Ontario Premier Doug Ford, centre, with Transport Minister Caroline Mulroney, left, march in York Region's Pride parade. (Kelda Yuen/CBC)

Beyond Scheer, former prime minister Stephen Harper also stayed away from Pride marches.

Some provincial conservative leaders have been more willing to participate in Pride. Ontario Premier Doug Ford marched in York Region Pride last year. His predecessor, Patrick Brown, also led a Progressive Conservative delegation at Toronto Pride in years past.