FREDERICTON -- The high-stakes political manoeuvring continues in New Brunswick, with Liberal Premier Brian Gallant seeking a formal alliance with the Greens -- and another potential king-maker saying he'll work with any party.

Flanked by his new caucus members Wednesday, Gallant said they had decided to reach out to the Green party.

"I think it would then be important to have a discussion on exactly what this would look like, what mechanism would be used, what we could agree on, what we would put aside from each of our platforms and exactly how we could have some kind of relationship in the legislature," Gallant said.

He said the Liberals had not yet made an overture to the small party, and the Greens themselves were non-committal about how they might proceed after Monday's deadlocked election results.

The Liberals won 21 seats -- one fewer than Blaine Higgs' Progressive Conservatives -- but Gallant remains premier as he tries to get support from other parties to maintain the legislature's confidence. He said he will call the house back before Christmas.

Both the left-of-centre Greens and right-of-centre People's Alliance won three seats each, making them both potentially very powerful in a minority legislature.

People's Alliance Leader Kris Austin said Wednesday he's willing with any party to make a minority government work -- and said it's unfortunate that Gallant has said the Liberals would not form a coalition with his party.

"We understand that the people of New Brunswick have given all of us a mandate to work together," Austin said.

"That requires negotiation. That requires give and take. I'm willing to do that, and I think if the other parties are not willing to do that, I think New Brunswickers will see that for what it is as well."

Green Leader David Coon has been meeting with his new MLAs to discuss their next steps. On Wednesday, he said the legislature session will be a real test, especially for the mainline parties.

"The others keep talking about doing politics differently but they never do. So I see that we as a Green caucus have a real opportunity here to help make that happen where we create a legislative assembly that actually starts to co-operate on behalf of the people of this province," he said.

Coon said there are similarities in all the parties' platforms, and he's sure they can all find issues to support.

"Take the People's Alliance even. They have a clear policy against spraying glyphosate over the forests. We agree with them. That's a particular issue we could co-operate with them on. The Tories seem to be leaning in that direction too, so that's interesting," Coon said.

But Coon made it clear the Green party is not willing to compromise on linguistic rights. The People's Alliance has called for efficiency in the delivery of services and not just what is known as "duality," particularly in health and education.

Austin said party leaders need to put aside egos and agendas to make a minority legislature work.

"I think that's why Mr. Gallant is having such a tough time because they're used to running New Brunswick with an iron fist and now they don't have that option," Austin said.

Robert Gauvin, a francophone who won the Tories' only northern seat, has said he's opposed to the positions of the People's Alliance, but Higgs says Gauvin is "fully onside."

Higgs was also asked about some kind of alignment with the People's Alliance.

"Alignment is a strong word," he said Tuesday.

"My goal is to go down through the platforms of each party and to say OK, where do we have common ground? Where do we have issues that we just aren't going to change anything on our behalf -- this is what we believe in and this will stay solid, and I think certainly linguistic rights are a clear example of that," Higgs said.

"We have aims and principles in our party that are foundational and we are not going to be changing that."

Austin said some people are fear-mongering, accusing his party of being anti-French. But he said it fully supports both linguistic groups, and is willing to sit down to discuss that with anyone.

"We've been saying for many years we respect the rights of both francophone and anglophone citizens to receive government services in their language of choice," he said.

"What we want to do is make sure that it works in the best interest for all New Brunswickers so that we have more paramedics, more doctors, more teachers. The money we're spending on duality can be invested in frontline services while still maintaining the rights of both linguistic communities," Austin said.

On election night, Gallant ruled out the possibility of a coalition government with the People's Alliance.

"There are some fundamental values that I need to share with any party that we would be working with, and that's not the case there. With that said, if we put something forward and they vote for it, that's going to be their prerogative," said Gallant.

"I think that the alternative is Blaine Higgs and the Conservatives will try to form an alliance with the People's Alliance. I obviously don't think that's what's right for our province. I think that would bring some of the policies a lot more right than people wanted."

Prime Minister Justin Trudeau, asked whether it was Gallant or Higgs who controlled New Brunswick, said simply Wednesday: "We have a strong Constitution and parliamentary precedent that will help them work this out."