The Trump administration intends to push to renegotiate the U.S. trade deal with Canada and Mexico ahead of a required 2026 review of it, seeking to shore up U.S. auto jobs and counter Chinese firms that are making inroads into the Mexican auto sector, people familiar with the deliberations said.

The U.S.-Mexico-Canada Agreement, which Mr. Trump signed in 2020, required the three countries to hold a “joint review” of the deal after six years, on July 1, 2026. But Mr. Trump intends to begin those negotiations sooner, according to the people, who spoke on the condition of anonymity to discuss plans that had not been made public.

Trump officials particularly want to tighten the pact’s rules governing the auto sector, to try to discourage auto factories from leaving the United States, they said. They are also seeking to block Chinese companies making cars and auto parts from being able to export to the United States through factories in Mexico.

Mr. Trump has also threatened to impose a 25 percent tariff on products from Canada and Mexico, saying those countries are allowing drugs and migrants to flow across American borders. Speaking from the Oval Office on Monday night after his inauguration, he said he planned to move forward with the tariffs on Feb. 1.

Members of the Trump team believe that Mexico has been violating the terms of a separate agreement to limit metal exports to the United States, and they are eager to show the Mexican government that they mean to take action against such trade violations, one person familiar with the conversations said.

The Wall Street Journal earlier reported that Mr. Trump was pushing for an early renegotiation of his North American trade deal. The three countries are required to meet to discuss the terms of the trade deal six years after the agreement went into force, but trade experts have expected the Trump team to speed up work on the issue.

Mexico and Canada had initially insisted on having six years elapse before the terms of the deal would be revisited because they thought that would get them through a second consecutive Trump administration, a person familiar with the negotiation said. Instead, the requirement for talks in 2026 will fall squarely in Mr. Trump’s lap.

Mr. Trump has long criticized the previous trade deal, the North American Free Trade Agreement, and his officials negotiated their new deal to replace and update it. One of the pact’s major changes was raising the threshold of a vehicle’s content that needed to be produced in North America to qualify for zero tariffs. The deal also included other provisions requiring carmakers to use more North American metal and higher-paid workers.

But Mr. Trump and his advisers now think those terms have not been restrictive enough to prevent car manufacturers from moving factories outside the United States. They have also been wary of a surge in Mexican imports of cheap and high-quality Chinese vehicles, as well as Chinese efforts to set up auto factories in Mexico.

Speaking at the Detroit Economic Club in October, Mr. Trump said that “Mexico is becoming the second China.”

“When China comes in, they take over everything, and you’d have no car manufacturing anymore,” he added.

People familiar with the plans cautioned that they could still change. It also remains to be seen whether Mr. Trump is threatening tariffs against Canada and Mexico as a negotiating tactic to extract certain concessions from their governments, or would simply impose them outright. The Trump administration’s press office did not immediately respond to a request for comment.

Mr. Trump signed an executive order on Monday evening directing various agencies to study a wide variety of trade issues. He did not immediately impose any new tariffs, as he had threatened previously, but the order teed up the possibility of a host of trade actions in the months to come.

One provision in the order directed trade officials to assess the impact of the North American trade deal on workers, farmers and other businesses and “make recommendations regarding the United States’ participation in the agreement.” It also directed them to begin soliciting public comments in preparation for the July 2026 review of the trade deal.