It was a passing remark which almost went unnoticed amid the bluster and hyperbole of Donald Trump’s rambling press conference this week, but the president has yet again cast doubt on the future of critical free trade talks between Canada and the US.

Despite a US-set deadline of 30 September to rewrite the North American Free Trade Agreement (Nafta), negotiations have by all accounts come to a standstill. The American trade delegation recently signed a revised free trade agreement with Mexico – but Canada has been left waiting for its own deal.

“We’re very unhappy with the negotiations and the negotiating style of Canada – we don’t like their representative very much,” Trump told reporters on Wednesday, in an apparent reference to Canada’s foreign minister, Chrystia Freeland.

Trump also claimed that he turned down a meeting with Justin Trudeau to discuss the prospects of a deal “because [Trudeau’s] tariffs are too high and he doesn’t seem to want to move – and I told him: ‘Forget about it.’”

Canadian officials were quick to deny that Trudeau ever requested a meeting.

But the Canadian prime minister insists that he remains committed to the talks – and the prospect of a breakthrough. “The Americans are finding that the negotiations are tough because Canadians are tough,” Trudeau said on Thursday. “But a good, fair deal is still very possible. We won’t sign a bad deal for Canadians.”

The stalled trade negotiations – and Trump’s comments – have renewed whispers of personal friction between Freeland and US trade representative Robert Lighthizer.

One person familiar with the two envoys described them as “chalk and cheese”: Lighthizer, a mercantilist trade lawyer from the American rust belt, and Freeland, a former globetrotting journalist with a keen interest in foreign policy and multilateralism.

Chrystia Freeland. Canadian officials insisted her relationship with the US was ‘cordial’. Photograph: Chris Wattie/Reuters

Earlier in the summer, Freeland set off a diplomatic firestorm when she tweeted support for jailed Saudi human rights activists – and refused to back down from her position after Riyadh expelled Canadian diplomats and curtailed trade.

Lighthizer reportedly prefers a more subdued – but forceful – approach to negotiations. He has moved quickly to finalize a trade deal with Mexico that makes no mention of Canada, shattering the notion of the “three amigos” pact that once governed free trade across the continent.

Canadian officials pushed back on the notion that the relationship had become acrimonious. “Look, it’s a negotiation,” said one official familiar with the talks, adding that disagreements should not be mistaken for animus – and insisting that Freeland’s relationship with her US counterpart continued to be “cordial”.

Lighthizer has previously stated that he and Freeland get along well, calling her a “good friend” in response to press reports that he disliked her. People familiar with the trade talks say he prefers dealing with Freeland instead of Canada’s chief trade negotiator, Steve Verheul.

Kelly Knight Craft, US ambassador to Canada, downplayed Trump’s criticisms of Freeland at a reception in Ottawa on Wednesday. According to those present, Craft described the Canadian ambassador as “articulate” and “smart”.

But that same evening, Canada’s ambassador to the US, David MacNaughton, told a Toronto audience that the chance of reaching a deal on Sunday was “50/50”.

The US and Canada remained deadlocked over various trade provisions. Initially, Canada balked at lifting protectionist policies that support its dairy farmers, which heavily taxes imports of cheese and milk.

More recently, Canada has pushed back on any new deal that would not provide explicit protections from US tariffs on steel and protections from punitive tariffs on autos.

In June, the US abruptly lifted Canada’s exemption from steel and aluminum tariffs on the grounds of national security – a move which Trudeau described as “insulting”.

“The president was using tariffs as a tool to squeeze the Canadians,” said Bruce Heyman, former US ambassador to Canada. “Canada is very close to getting a deal, but wants assurances from the United States that they’re not going to place tariffs on them going forward,” he said, calling demand for protection from future duties as “awfully reasonable”.

With Trump’s use of tariffs as a negotiating tool, Canadian worries its auto sector – a critical part of the country’s economy – could be the next target.

Economists have warned Trump’s threat of a 25% tax on Canadian cars would devastate the country’s manufacturing sector and usher in a recession.

While the full text of its new trade agreement with the US has to be released, Mexico never won protection from future tariffs, said Heyman. “I think the Canadians are in a good spot to sit down and make appropriate requests now.”

Another sticking point for Canadian officials has been a mechanism that would allow trade arguments – like the tariffs – to be mediated.

“There are things where basically we are not willing to give in to, because it would render the agreement meaningless,” MacNaughton told the Toronto audience on Wednesday. “I mean, if you can’t resolve disputes in a fair and balanced way, then what’s the use of the agreement?”