Mexico’s president offered a warning last month in response to news that the Trump administration planned to designate drug cartels as terrorist groups.

“If they declare these criminal groups as terrorists, then we’ll have to expand our U.S. lawsuit,” Claudia Sheinbaum, Mexico’s president, said at a news conference.

She was referring to an unusual lawsuit that will be heard by the Supreme Court on Tuesday in which Mexico argues U.S. gun manufacturers have aided in the trafficking of weapons used by the cartels.

The case reverses longstanding complaints by President Trump that Mexican cartels have contributed to rising violence in the United States. Instead, Mexico argues the majority of guns found at Mexican crime scenes come from the United States. It seeks some $10 billion in damages from U.S. gun makers.

The dispute comes before the justices at a time of heightened tension between the two countries as the Trump administration leans on Mexico to crack down on illegal migration and cartel organizations. Tariffs on imported goods from Mexico are scheduled to go into effect on Tuesday — the same day the justices are set to consider the guns lawsuit.

President Trump has cited drug trafficking from Mexico as one of the factors driving the decision to impose tariffs. His administration has taken a number of steps to push back on the cartels, including designating more than a half-dozen of the criminal groups as foreign terrorist organizations. That move could result in penalties, including criminal charges, for companies found to be entangled with the cartels, but it has also raised concerns from the Mexican government of a potential violation of Mexico’s sovereignty.

Lawyers for Mexico argue that U.S. manufacturers and gun dealers are complicit in what they call an “iron river” of firearms pouring into the country and arming cartels. They point to strict controls on gun purchases in Mexico, where civilians are not allowed to purchase the types of rapid-fire, powerful military-style weapons favored by the cartels, as evidence that as many as half a million firearms are smuggled from the United States into Mexico each year.

“It is far easier and far more efficient to stop the crime gun pipeline at its source and to turn off the spigot,” said Jonathan Lowy, president of Global Action on Gun Violence and a longtime litigator against the gun industry who has worked on the case on behalf of Mexico.

The gun makers, joined by a slew of gun groups including the National Rifle Association, have argued the lawsuit would undermine gun rights in the United States.

“Mexico has extinguished its constitutional arms right and now seeks to extinguish America’s,” the N.R.A. said in a brief in support of the gun makers. “To that end, Mexico aims to destroy the American firearms industry financially.”

The case may be viewed skeptically by the Supreme Court, where the 6-3 conservative supermajority has worked to expand gun rights. But at a time when Mr. Trump has targeted the country, it has offered a forum for Mexico to publicize its counter case that U.S. gun manufacturers share the blame for cartel violence. The Mexican government has also sued several gun stores in Arizona and could expand the effort by filing additional suits.

At a conference last month in Latin America, Pablo Arrocha, a legal adviser for Mexico’s foreign ministry, said that two lawsuits filed so far marked only the beginning of a broader legal strategy to push back against the flow of guns across the border.

For years, Mexico has pushed the United States to do more to curtail the trafficking of American manufactured guns over the border. When Mr. Trump announced he would delay tariffs against Mexico earlier this month, both nations had agreed to address their respective concerns: Mexican authorities promised to work to stem the flow of drugs across the border while U.S. authorities would try to combat gun trafficking.

In recent days, there have been signs of improving relations between the two countries, including when the Mexican government this week sent to the U.S. nearly 30 top cartel operatives wanted by the American authorities. But inside the White House, Mr. Trump’s advisers remain split over whether to take more substantial action in Mexico, including carrying out military strikes against Mexican drug cartels.

A White House spokesman did not respond to a request for comment.

Mexico first sued multiple gun companies in 2021, arguing that the cartel bloodshed was “the foreseeable result of the defendants’ deliberate actions and business practices.”

A trial court judge dismissed the case, finding it was barred by a 2005 federal law that limits litigation against gun manufacturers and distributors and has provided immunity from actions brought by the families of people killed and injured by their weapons.

A unanimous panel of judges of the U.S. Court of Appeals for the First Circuit, in Boston, overturned that decision. They found that the lawsuit met the criteria for a part of the law allowing for litigation in cases where knowing violations of firearms laws are a direct cause of the plaintiff’s injuries.

Gun makers asked the justices to hear the case, Smith & Wesson Brands v. Estados Unidos Mexicanos, No. 23-1141. Lawyers for Smith & Wesson argued Mexico had presented a legal theory that was an “eight-step Rube Goldberg, starting with the lawful production and sale of firearms in the United States and ending with the harms that drug cartels inflict on the Mexican government.”

The lawyers contend the gun makers acted lawfully in the United States and cannot not be held responsible for illegal cartel behavior in Mexico. They cited a 2023 Supreme Court case in which the court ruled unanimously that social media companies could not be sued for aiding terrorism because they hosted posts from ISIS.

A trial court judge dismissed Mexico’s case against six of the defendants on other grounds, leaving the Supreme Court’s decision in the case to apply to claims against Smith & Wesson, a gun manufacturer, and Interstate Arms, a wholesaler.

Zolan Kanno-Youngs contributed reporting.