Perdue said on C-SPAN that Lighthizer has been "very clear" about the need for the Class 7 pricing system to be repealed.
"We have been very clear on that, that there can not be more access given", Wiens said in a telephone interview.
The U.S. has said it plans to present Congress with the deal it has with Mexico if Canada doesn't get on board.
Officials have identified the main sticking points as Canada's dairy quota regime, Ottawa's desire to keep a trade dispute-resolution mechanism and Canadian media laws that favor domestically produced content.
Yet, he stressed that "if we sign the deal it'll be. for Canada and Canadians".
Canadian Foreign Minister Chrystia Freeland said told reporters after a two-and-a-half-hour meeting with U.S. Trade Representative Robert LighthizerRobert (Bob) Emmet LighthizerMcConnell urges GOP senators to call Trump about tariffs Companies brace for trade war MORE that a deal is "eminently possible" but said she would not negotiate the pact in public, the CBC reported. Overall, he said, he believes Canada is handling the talks well. Under U.S. trade negotiating laws, a text for that agreement is due by October 1.
"That has been the right decision", Freeland said late Tuesday of the mutual agreement to avoid publicly disclosing details of the talks.
"We're negotiating all this at once".
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One of the sticking points is access to the Canadian market for U.S. dairy farmers.
Canadian officials have said they are working on the assumption that they have until the end of September to make a deal.
Freeland returned to Washington on Tuesday to continue meeting with her U.S. counterpart.
"Maybe that helps us all put into perspective the negotiations that we're having - and also put into a little bit of historical perspective the importance and the significance of the relationship between Canada and the United States", she said of the anniversary.
"The U.S. knows what Canada's tough issues are, so they're going to hold those to the end, and squeeze out concessions on every other issue they can", said Ujczo, who is regularly briefed on the talks.
Republican Tom Reed, a member of the Committee of ways and means of the House of representatives, said in a television interview broadcast on Sunday that provide a larger market access to u.s. dairy producers could appease president Donald Trump. Freeland spent a day in Washington last week and said she and Lighthizer were making very good progress in some areas, although a deal remained out of reach.
U.S. President Donald Trump has threatened to push ahead with a bilateral deal with Mexico, effectively killing the nearly 25-year-old three-country NAFTA pact, which covers $1.2 trillion in trade.
The hope is for a trilateral agreement in principle that Congress can approve before Mexico's new president takes office on December 1.