Saskatchewan's next premier has promised there will be a healthier relationship between his province and the federal government, now that his centre-right party is in power.

"We have a lot of contacts, certainly, with those who serve in the national government and the members of Parliament for this province," Brad Wall said at a news conference on Thursday.

"I would expect that those would be an advantage.'"

Wall's Saskatchewan Party ousted Lorne Calvert's NDP party after 16 years of forming government on Wednesday. The Saskatchewan Party is a 10-year-old coalition of former Progressive Conservatives, former Reformers and right-wing Liberals.

Wall left open the possibility of turning away from a constitutional challenge made by Lorne Calvert's NDP government over federal equalization formula.

The province has maintained it is being short-changed by the way the transfer formula treats natural resource revenues. Calvert asked the Court of Appeal to rule on whether Saskatchewan had a case before the election campaign began.

"I've said from the beginning that I want to see the legal opinion," he said. "Saskatchewan does need leadership that acts like it is leading a have province and a province that intends to remain a have province."

On Wednesday night, Wall told his supporters, "And now for something completely different!" -- a nod to the Monty Python's Flying Circus phrase.

The Saskatchewan Party captured 37 seats of 58, leaving the NDP with 21 seats. The Liberal Party remained shut out for a second consecutive election.

In doing so, the Saskatchewan Party captured more than 50 per cent of the vote, compared to about 37 per cent for the NDP. The Liberals captured about nine per cent of the vote and the Green Party about two per cent.

Prime Minister Stephen Harper congratulated Wall in a statement Thursday. The Tories hold 12 of 14 federal seats in Saskatchewan.

"Premier-elect Wall has been given a mandate to address the issues of importance to all the people of Saskatchewan, and I look forward to working with him to build a strong Saskatchewan in a strong Canada," Harper said.

Ken Rasmussen, a political analyst at the University of Regina, said managing Saskatchewan's current economic boom was a major campaign issue, along with health care.

Wall had made promises to reduce wait times, a vow that's proved difficult for other premiers to carry out in other provinces, he noted.

NDP Leader Lorne Calvert, the current premier, had made an election promise to cap drug prescription costs at $15.

Rasmussen said that proved to not be a big health-care priority for Saskatchewan voters.

In his acceptance speech, Wall talked about improving health care, fixing roads, cutting property taxes and giving more money to schools.

He also stressed the need to keep young people in the province.

"We made a commitment to implement what will be in this country the most aggressive youth retention plan to keep our young people here, to encourage youth entrepreneurship," Wall said.

In defeat, Calvert told his supporters in Saskatoon on Wednesday that the party could hold its head high.

"Our province .... tonight is stronger, more optimistic and more hopeful than before we came," said Calvert, party leader and premier since 2001.

"The lives of many families in our province are better tonight than they were four years ago. Our children are coming home, our Aboriginal people are gaining strength, our province is greener, our province stands taller in Canada, and together we have built a solid foundation for the future based on our values."

However, the 54-year-old one-time United Church minister told reporters that it wasn't likely he would lead his party into another election.

"I'm going to sit down with the party. The likelihood is not great that I would lead the party in the next election, but that decision is not made."

David Karwacki, the Liberal leader, promised to hold the new Sask Party government to account even though he failed to gain a seat in the legislature for the third straight time.

"We are going to continue to fight for everyday working people, that's what the Liberal party is about. It's about building the skills in everyday working people so they can succeed in Saskatchewan, so this boom doesn't leave people behind," he said Wednesday.

With respects to his own future, Karwacki said, "We'll pick up the pieces, I'll talk to Liberals and we'll go from there."

Wall said Thursday his government will no longer support an appeal filed against the federal government and its plan to eliminate the board's western barley marketing monopoly.

He also said that when his party forms government on Nov. 21 they will introduce legislation to establish fixed election dates every four years. That would make the next election Nov. 7, 2011.

With files from The Canadian Press