Canada's Prime Minister Justin Trudeau (R) meets with U.S. President Donald Trump during the G7 Summit in the Charlevoix town of La Malbaie, Quebec, Canada, June 8, 2018.

The U.S. and Canada agreed on Thursday to continue negotiating a new NAFTA deal, amid a tense trade environment that includes an announcement Friday of new U.S. tariffs on China.

U.S. Trade Representative Robert Lighthizer and Canadian Foreign Minister Chrystia Freeland agreed to continue negotiations toward a revised North American Free Trade Agreement, despite frayed relationships between the U.S. and Canada following President Donald Trump's rebuke of Prime Minister Justin Trudeau last weekend.

The chilled atmosphere, which included Trump trade advisor Peter Navarro insulting Trudeau, led to speculation that the talks would die and Trump would withdraw the U.S. from NAFTA altogether. Freeland said no specific date was yet set to continue talks but said negotiators will be working hard over the summer. Mexican officials have said talks may continue in July.

Trump's already testy meeting with leaders of major trade partners at the G-7 summit last weekend took an even more difficult turn when he and administration officials slammed Trudeau.

For his part, Trudeau had commented that Canada would not be pushed around by the U.S. and that it would proceed with retaliatory tariffs. That drew criticism from Trump and other officials who said Trudeau was stabbing Trump in the back.

Freeland spent the week meeting with officials in Washington, and met with Lighthizer Thursday. According to Reuters, she said she and Lighthizer agreed to continue negotiating a new NAFTA accord.

The White House is moving forward on another front, with plans to roll out tariffs Friday on a truncated list of Chinese exports, three sources familiar with the matter told CNBC.

The list is expected to include between 800 and 900 products, compared with the original list of about 1,300 products published by the U.S. trade representative in April. The dollar value of the goods the Trump administration expects to target is unclear.

Dan Clifton, head of policy research at Strategas, said he expects the list to be shorter than proposed and possibly affect $40 billion worth of goods.

"The list is likely to be less than the original $50 [billion] proposal and the net tariff impact will likely be around $10 [billion] (25% on $40 [billion] worth of goods). The Trump Administration is likely to implement the tariffs next week absent some deal in the coming days," Clifton wrote Thursday.

China has threatened its own tariffs, as have other trading partners the Trump administration has targeted. Progress appeared to be made when the White House struck a deal to allow China's ZTE to resume buying U.S. components even though it violated sanctions against selling to Iran and North Korea. However, the deal now is in question, with the Senate attempting to undo it with a bill that is making progress, but the White House is attempting to have lawmakers strike it before Congress passes a final version.

"That is a cornerstone of what President Trump promised President Xi," said Juan Carlos Hartasanchez, senior director with Albright Stonebridge Group. "I think for the Chinese, they just look at these guys and say they are not aligned. They don't have a direct message and that is likely something that debilitates the U.S. in the eyes of the Chinese."

Hartasanchez, who follows NAFTA, said it would help the NAFTA discussions, though maybe not the outcome, if the U.S. were to find a way to settle its disputes with China.

"They have opened too many fronts in battles against the main trading partners. They opened a front with China, they have the NAFTA front, and they opened a battle with Europe. It doesn't allow you to measure the effect of one negotiation on the others," he said.

Political and trade strategists say the fate of NAFTA is more unclear after G-7, and it is now more difficult than ever to handicap the odds of an agreement to revamp the 24-year old trade pact.

Navarro appeared to be toning down the administration's rhetoric Tuesday when he apologized for insulting Trudeau by saying there was a special place in hell for him. Navarro also said the list of proposed tariffs on Chinese goods would be smaller than the original list.