Like most US congressional Republicans, Mexican and Canadian officials are also wary of major changes that could hurt their exports to the USA or even alter the three-way framework that underpins Nafta.
The Trump administration also wants to change the dispute resolution mechanisms set up under the agreement.
Still, the president's plans to rework NAFTA have drawn cautiously optimistic support.
Canada and Mexico are America's second and third largest trade partners after China.
US Trade Representative Robert Lighthizer formally notified Congress of the intent to revamp the pact with Canada and Mexico, which accounts for about $1 trillion in annual trade.
Over the next 90 days, Lighthizer will consult with lawmakers on the position the USA will take in negotiations, which could begin as early as August 16.
"We look forward to working with the administration to strengthen the agreement in a seamless way and ensure that we retain the current benefits for American workers, farmers and businesses", says Texas Republican Rep. Kevin Brady, chairman of the House Ways and Means Committee.
"We are going to give renegotiation a good strong shot", Lighthizer said. TPP's goal was precisely to establish a modern approach to free trade by encompassing new products and services - sectors in which the US has most to gain - and by making labor and environmental standards easier to enforce. He promised a very aggressive negotiating schedule to conclude the talks as quickly as possible.More news: The Coca-Cola Target of Unusually High Options Trading (KO)
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"The trilateral agreement has been an enormous benefit for all parties", Mexico's economic ministry said in a statement.
"The agreement is trilateral and should continue to be a trilateral platform. Why?" "In particular, we note that NAFTA was negotiated 25 years ago, and while our economy and businesses have changed over that period, NAFTA has not".
Lighthizer says he spoke with his counterparts in Mexico and Canada, adding all three nations will benefit from the renegotiation.
"If I'm unable to make a fair deal, if I'm unable to make a fair deal for the United States, meaning a fair deal for our workers and our companies, I will terminate NAFTA", Trump said on April 27 in remarks during a meeting with the president of Argentina. But the president ultimately said he planned to renegotiate the agreement. "While the NAFTA notice lacks many specifics, this union will head into discussions with clear objectives that will put the needs of the people above those of the powerful".
The Mexican government said Thursday says it "welcomes" the opportunity to renegotiate NAFTA.
Canadian Foreign Minister Chrystia Freeland said in a statement that the trade agreement had resulted in economic growth and the creation of millions of jobs.
Ms Freeland said in a statement on Thursday that the country remains "steadfastly committed to free trade in the North American region".
She says almost nine million United States jobs depend on trade and investment with Canada.