The four men vying for the leadership of Alberta's new United Conservative Party focused their attacks on Alberta's NDP government and Prime Minister Justin Trudeau rather than each other during the first official debate Wednesday.

Brian Jean, Jason Kenney, Doug Schweitzer and Jeff Callaway sought to persuade party members crammed into a Calgary concert hall that they have what it takes to oust Premier Rachel Notley in 2019 and fight for Albertans' interests in Ottawa.

The candidates took turns promising to undo the provincial carbon tax, decrying a hike in the minimum wage and pledging to get Alberta's fiscal house in order by reining in spending.

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There were also swipes at the federal equalization program — through which payments are meant to even out fiscal disparities between so-called "have" and "have-not" provinces — and Ottawa's lack of action of building new market-opening pipelines.

"This leadership race is about who can guarantee defeat of the NDP in the next election and I am the only candidate who is here today who can win seats in every single region of the province," Jean, the former leader of the Wildrose party, said in his opening remarks.

Kenney, the former federal Conservative cabinet minister who spearheaded the drive to unite the Wildrose and the Progressive Conservatives, touted his years of experience in Ottawa.

"Who has the right kind of experience, temperament and skills to be a strong conservative premier, to hit the ground running on Day 1?" he asked.

"Who has the experience to take the fight to Justin Trudeau and stand up and defend our province?"

Just moments after it concluded, Kenney's team issued a news release declaring he was the "clear winner" of the debate. A short time later, Jean's campaign issued its own statement declaring victory.

Schweitzer, a lawyer and long-time conservative strategist, has sought to set himself apart as the most progressive candidate when it comes to social issues, such as support for LGBTQ rights.

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He said he recently met a supporter whose young daughters liked the UCP's economic views, but refused to back the party because they were unsure of where it stood on gay-straight alliances in schools.

"I want to make sure we get these issues right," he said, saying that if the party is vulnerable on social issues, it will play into the NDP's hands.

"Because if we do that, we'll be able to engage the millennials, we'll be able to turn the page on social issues and keep the focus of the next election campaign on the economy, which is where it should be."

Jeff Callaway, former president of the Wildrose party, said conservatives have nothing to be ashamed of and everyone — including social conservatives — should have a voice in the party.

Callaway, who describes himself as a social moderate, said it would take "consistent and principled leadership" to defeat the NDP in 2019 and stand up to Trudeau.

"We need a leader who can debate Rachel Notley and win. We need a leader that Albertans don't have to wonder what side of an issue they'll stand on today."

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Callaway was the only candidate to take major swipes at a leadership rival on stage.

He argued Jean believed he had more power in the Wildrose as leader than grassroots members.

"He's actually a good guy. It's just that we have very different styles of leadership," Callaway told reporters after the debate.

There will be four more debates - in Edmonton, Red Deer, Fort McMurray and Lethbridge - before party members pick a leader next month.

Mount Royal University political scientist Lori Williams suggested before the debate that the candidates shouldn't focus too much on vilifying the NDP.

"No government in waiting can be successful if all they're doing is just criticizing what the people there now are doing," she said. "They've got to offer a credible, appealing alternative."