Quebec Premier Philippe Couillard fought back Tuesday against criticism of his government's handling of the recent wave of asylum seekers crossing illegally into Quebec from the United States.

Couillard questioned the human rights commitments of both the Opposition Parti Québécois and the Coalition Avenir Québec, pointing to recent comments by their leaders, Jean-François Lisée and François Legault.

He accused both men of showing "either ignorance or the perception of ignorance about fundamental human rights" that Quebec has a legal responsibility to respect and uphold.

"Canada signed the 1951 Geneva Convention on Refugees that manages the flow of people between countries who want to claim asylum," he said.

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The president of the union representing Canada's border guards says wait lists for processing asylum claims are getting longer and could explode if more resources aren't dedicated addressing the influx at the Quebec border. (Graham Hughes/Canadian Press)

"Apparently, Mr. Lisée might prefer that [Quebec] pull out of the Geneva Convention. If so, he should make that clear."

Couillard was referring to a tweet by Lisée on Monday that noted a new poll showing that 51 per cent of Quebecers were in favour of preventing illegal border crossings. Lisée also claimed an independent Quebec would make people respect its border.

Couillard said people who were claiming asylum in Canada were not in the country illegally, despite the impression that he insisted Lisée and Legault were creating.

"It's wrong to say they're here illegally," he said. "What's illegal is preventing them from staying and claiming asylum."

He invited both Lisée and Legault to "get reacquainted with the conventions, and the law" and said such claims by his political opponents will only fuel anti-immigrant feelings and anxiety in the province.

When asked by a reporter about signs by an anti-immigrant far-right group that have been popping up around Quebec City in recent days, Couillard was equally unhappy, but noted the importance of free speech.

"I've said before that free speech allows for nonsense," he said. "It falls to us to reply with wisdom, balance and truth."

Lisée accuses Couillard of twisting words

Lisée, meanwhile, issued a lengthy Facebook post Tuesday in which he accused Couillard of twisting his words.

He said an independent Quebec would force people to respect the border in accordance with international treaties that oblige it to "welcome asylum seekers and process their claims."

"However, contrary to Canada, Quebec would welcome them at regular border crossings, not in the woods."

Lisée was referring to the argument he's been making recently that Canada should pull out of its Safe Third Country Agreement with the United States. The agreement means most asylum claims made at regular border crossings are turned down.

"It's pure intellectual dishonesty," he said of Couillard's criticism.

However, asylum claims made after crossing illegally into Canada still have to be heard.

Both Couillard and representatives of the federal government have said pulling Canada out of the Safe Third Country Agreement — which deems both Canada and the U.S. safe for refugees — would damage diplomatic relations between the two countries.

Couillard has made clear that he disagrees with the proposal.

Lisée wants a wall, Couillard says

On Tuesday, Couillard said Lisée's claim that an independent Quebec would keep people from crossing illegally into the province would leave little option but to build a wall.

"It sounds like he wants a wall when you look at it, because it's a long border and how are you going to prevent people from crossing between official border crossings? It would take a wall."

Canadian Army assembles tents at Quebec border0:17

The exchange comes amid new concerns voiced by the president of Canada's border guards union, Jean-Pierre Fortin, about the situation at Quebec's Saint-Bernard-de-Lacolle border crossing, where asylum seekers crossing illegally nearby are taken for processing.

In an interview Tuesday, Fortin said conditions there are deteriorating despite the establishment of two Canadian army-built temporary camps and a third that is underway.

"Yesterday, there were 300 people sleeping on a loading dock and another another 150 to 200 people sleeping inside in difficult circumstances," he said.

"These people are ultimately our responsibility and the logistics around this are extremely complicated."

Fortier said 480 asylum seekers crossed the border illegally on Monday alone, but the CBSA and immigration officials only have the capacity to treat 200 claims a day "at best."

"So, each day the lists get longer, the wait times get longer, and the difficulties remain," he said, warning that the wait times are threatening to explode.

With files from Radio-Canada