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President Trump announced on Wednesday he rejected a meeting with the Canadian Prime Minister this week, as the countries struggle to strike a new North American trade agreement before a self-imposed October deadline.

Fox Business reporter Susan Lee asked Trump in a press conference at the United Nations General Assembly in NY. The president said it would be called "USM", for the US and Mexico, instead of "USMC", and offered blunt criticism of the Canadian team engaged in the talks.

"Yeah, I did", he told a news conference in NY when asked by a reporter whether he had rejected a one-on-one meeting with Mr Trudeau.

He said the U.S.is "very unhappy with the negotiations and the negotiating style of Canada".

Trump's comments on Wednesday were just the latest in a string of attacks he has leveled against Trudeau and Canada this year.

"The Americans are finding that the negotiations are tough because Canadians are tough negotiators, as we should be", Trudeau told reporters on the way into a regular weekly cabinet meeting in Ottawa.

"With Mexico, we're not going to say: "No deal" because of Canada", Lighthizer said.

"That's the motherload, that's the big one", Trump told reporters.

As reported by Reuters, US officials are complaining that Canada is refusing to make necessary concessions in order to achieve a trilateral pact that will update and replace NAFTA. Trudeau spokeswoman Chantal Gagnon said: "No meeting was requested".

The prime minister made the comment after being asked about USA trade ambassador Robert Lighthizer's recent glum assessment of the talks, which remain deadlocked over issues like dispute resolution, access to Canada's dairy market and the so-called Section 232 tariffs on Canadian steel and aluminum.

It's also not certain whether Trump's bilateral deal with Mexico will be approved, given Congress had authorized fast-tracked negotiations for a trilateral - not bilateral - trade deal.

The Canadian leader added existing United States tariffs on Canadian steel and aluminium, which were implemented in late May, would have to be scrapped before Canada felt confident in signing a new NAFTA agreement. "His tariffs are too high and he doesn't seem to want to move".

The deal with Mexico left open the question of whether Canada, the third country in NAFTA, would agree to the changes.

"If Canada doesn't make a deal with us, we're going to make a much better deal", he said.

"On steel and aluminum on this point, we started off trying to have some kind of overall agreement that would accomplish that". The U.S. president stayed seated as he extended his hand for a cursory handshake.

The UN encounter comes as the countries bear down on a USA deadline for a new NAFTA pact, but they remain divided on a handful of core issues.

Disputes have also arisen between over President Trump's request for increased access to Canada's protected dairy market.

"We're in dialogue with the Italian government to help them get maximum information about how this is benefitting Italy, and what Italy can do to take advantage of it", she said. "It was an interaction like so many are (at the) United Nations - quick but cordial". Trump spoke to both for longer than he did Trudeau.

Contrary to Trump's claims, the Prime Minister's Office says that there was never a meeting requested with Trudeau to begin with.

The NAFTA impasse can't be helping matters, either.

Earlier on Wednesday, Trudeau shrugged off US pressure to quickly agree to a deal and indicated it was possible the three member nations might fail to conclude a new pact.

A Trump administration official said the text of the agreement with Mexico was set to be published on Friday.

"I think everybody knows what each other's position is on all of the major issues and I think it's really a question of whether or not the USA wants to have a deal". I must be honest with you, we're not getting along at all with their negotiators.