The Canadian prime minister, Mark Carney, has said that Alberta is “essential” to the country’s future, hours after the province’s leader moved the oil-rich region closer toward a referendum on independence.

Separatists in the western province spent months collecting signatures seeking to trigger a binding October vote on seceding from the nation.

On 4 May, they delivered their petition to provincial officials, insisting they had collected more than enough names to force a vote under Alberta law.

But an Alberta judge shut down the process, saying the citizens’ initiative was invalid because the separatists had failed to consult with Indigenous groups whose rights could be threatened if the province separated from Canada.

In an address late on Thursday, Alberta’s premier, Danielle Smith, called the judge’s decision “erroneous”, charging that it “interferes with the democratic rights of hundreds of thousands of Albertans”.

Smith, a conservative whose political coalition includes separatists, said she supports “Alberta remaining in Canada”.

But she insisted she would not let “a legal mistake by a single judge” quash a debate that needed to take place.

“It’s time to have a vote, understand the will of Albertans on this subject and move on,” she said.

In October, she plans to ask Albertans if they want her government “to commence the legal process necessary to hold a binding referendum” on independence.

Smith said she had structured her question such that it does not violate the judge’s ruling, because it “does not directly trigger separation”.

Carney, who spent most of his childhood in Alberta, responded on Friday in a taped video address from Parliament Hill.

“Canada is the greatest country in the world, but it can be better, and we’re working on making it better. We’re working with Alberta on making it better,” he said.

Alberta “is essential” to Canada’s future, he added.

Polls show that roughly 30% of Alberta’s 5 million people support independence, a record-high figure.

The separatist camp accuses Ottawa of stifling Alberta’s oil industry with excessive federal influence, while blocking investment over what they view as unreasonable concern about the environment.

Carney and Smith are working together on advancing a new oil pipeline, something resisted by Carney’s predecessor Justin Trudeau.

Smith has voiced hope that increased federal support for the oil industry could help tame separatist anger.