Open this photo in gallery New Brunswick Liberal Leader Brian Gallant and wife Karine Lavoie, right, addresses the media after meeting with Lieutenant Governor of New Brunswick Jocelyne Roy-Vienneau, in Fredericton, Sept. 25, 2018. James West/The Canadian Press

The day after New Brunswick elected its first minority government in nearly a century, both the Liberal and Progressive Conservative party leaders are claiming the premier’s chair.

Liberal Leader Brian Gallant, whose party won the second-highest number of seats, said after meeting with the province’s Lieutenant-Governor on Tuesday: “I am still the Premier until I lose the confidence of the legislature, which may happen.”

However, Progressive Conservative Leader Blaine Higgs, who declared victory on Monday night after learning his party had won more seats than the Liberals, told a Tuesday news conference: “The right thing to do would be to admit he’s lost the confidence of the province and step down.”

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The Liberals won 21 seats and the Progressive Conservatives took 22, while two other parties won three seats each.

With 25 votes required for a majority in the N.B. legislature, the balance of power is held by the Green Party and the People’s Alliance, a populist party formed in 2010 that attracted controversy during the campaign for its language platform, which included eliminating the bilingual province’s official language commissioner.

“We’re not at this stage prepared to enter into discussions about any kind of agreement with any of the parties,” said Green Party Leader David Coon, an incumbent who was a one-man caucus before the election. “We haven’t had a minority government since 1920 … so all of us are feeling our way along. There’s no rush here.”

Mr. Coon said that New Brunswickers “voted for change” and said “that means really thinking about embracing a different political culture in the Legislative Assembly where MLAs have more freedom to vote as representatives of constituents rather than just always towing the party line.”

Whatever form that takes will be healthy for New Brunswick’s democracy, said Donald Wright, a professor of political science at the University of New Brunswick.

“New Brunswick politics is always a revolving door between the blues and the reds. No one anticipated this,” he said. “But Darwin was right. Ecosystems need genetic diversity … finally, we have some in the legislature.”

Mr. Gallant, who entered the election seeking to become the first premier to win a second term since 2003, said New Brunswickers sent a strong message about working collaboratively that he “humbly” accepts.

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“The only people that got any mandate last night were the 49 women and men who were elected to represent their communities,” Mr. Gallant said. “There’s an indication … people want to see change in the way government in done in the province. They’re asking us to figure out as adults how we can govern together in the legislature. We will try to do exactly that.”

He began his day meeting with Lieutenant-Governor Jocelyne Roy Vienneau, who asked Mr. Gallant if he believes he has the confidence of the House, which Mr. Gallant said he intends to recall “shortly,” before the year’s end.

“He indicated he thinks so; however, more discussions are necessary,” said Tim Richardson, a spokesman for Ms. Vienneau. “Her Honour awaits his final decision.”

Philippe Lagassé, an associate professor at the Norman Paterson School of International Affairs at Ottawa’s Carleton University, confirmed the election did not automatically change Mr. Gallant’s status as Premier. “That’s the key piece of this puzzle,” Mr. Lagassé said.

While the Crown can dismiss a Premier, “it will only do so in the most extreme cases,” Mr. Lagassé said, adding that it is convention for a Premier to resign after a vote of non-confidence in the legislature.

“Brian Gallant has an opportunity now to try and work with one of the other parties to secure confidence,” Mr. Lagassé said. “I suspect that is the nature of the negotiation happening today.”

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Mr. Gallant said he has “left the door open to have conversations” with the Green Party but offered no further detail.

People’s Alliance leader Kris Austin declined an interview with The Globe and Mail on Tuesday.

The province’s chief electoral officer, Kim Poffenroth, told The Globe that there are at least two electoral districts that may see recounts. Those with a difference of 25 votes or less between the first- and second-place candidates are eligible. But recounts, she said, are not automatically triggered as some parties have suggested. Ms. Poffenroth said a judicial application must be made.

“At this time, there is no recount process under way,” she said.