That move leaves the ball in the White House's court to decide how it wants to proceed with negotiations. The White House and the Office of the U.S. Trade Representative declined to comment.

Despite making clear their opposition to the above demands, Canada and Mexico will not walk away from the negotiating table, these people said. In public comments Tuesday, they are expected to tout the progress of negotiations in small business and competition.

In the last week, U.S. negotiators have formally tabled demands that a new trade deal with Canada and Mexico favor American manufacturing and expire after five years if all parties do not renew it. Those proposals have been called "poison pills" by the U.S. Chamber of Commerce and "nonstarters" by participants in the talks.

Top trade negotiators from Canada and Mexico will meet Tuesday with the U.S. trade representative, Robert Lighthizer, and firmly reject the protectionist U.S. proposals floated in the current round of NAFTA negotiations, according to three people briefed on the countries' positioning.

Canada's Foreign Minister Chrystia Freeland (C) speaks before the start of a trilateral meeting with Mexico's Economy Minister Ildefonso Guajardo (L) and U.S. Trade Representative Robert Lighthizer during the third round of NAFTA talks involving the United States, Mexico and Canada in Ottawa, Ontario, Canada, September 27, 2017.

It remains to be seen how President Donald Trump, who has repeatedly slammed the 23-year-old trade agreement, will react to the position. In an Oval Office meeting with Canadian Prime Minister Justin Trudeau last week, Trump again threatened to scrap the free trade agreement if the countries cannot strike a deal to rework it.

"If we can't make a deal, it'll be terminated and that will be fine," Trump said. "They're going to do well; we're going to do well, but maybe that won't be necessary. But it has to be fair to both countries."

Most U.S. lawmakers and business trade groups have aligned themselves with Canada and Mexico in wanting to preserve the deal. A GOP aide told CNBC that the Ways and Means Committee has communicated with Lighthizer's office that a trade deal including the protectionist provisions put forward would not have enough support to pass Congress.

Business lobbies representing auto manufacturers and retailers have pushed out statements establishing their support for preserving the deal, while making changes to modernize it.

"A collapse of the NAFTA trade agreement between the United States and our two largest trading partners would be an economic catastrophe, with massive disruptions in agriculture and manufacturing and increased costs for American consumers," said Hun Quach, vice president of international trade policy at the Retail Industry Leaders Association "As retailers, we strongly urge all parties to preserve the parts of NAFTA that work for American businesses and to avoid proposals that would damage the U.S. economy and hurt American families."

Talks among staff negotiators from the three countries concluded Monday, with top leaders from the three countries meeting Tuesday before making public remarks. The fourth round of negotiations is concluding as the three nations push to meet a year-end deadline. Three additional rounds of talks are expected, for now. The final round had been slated for early December in Washington.

After the negotiations began this year, Trump derided NAFTA as the "worst trade deal ever made" and said the U.S. neighbors were "both being very difficult."

Canada was the United States' second-largest goods trading partner last year, while Mexico was the third, according to the office of the USTR. Mexico sent more goods to the U.S. in 2016 than every country but China.

Trump has focused his ire on trade deficits, which he says hurt the U.S. economy and American workers. The U.S. had goods trade deficits of about $63 billion and $12 billion last year with Mexico and Canada, respectively, according to the USTR.