MEXICO CITY — In the White House, President Trump was telling American chief executives that the days of being treated unfairly by Mexico — on trade, on immigration, on crime — were over.
“You see what’s happening at the border: All of a sudden for the first time, we’re getting gang members out,” Mr. Trump said. “And it’s a military operation.”
But in Mexico, his Homeland Security secretary, John F. Kelly, was saying the opposite, trying to tamp down fears of a military operation and assuring the public that American soldiers would not be used to police the border.
“I repeat: There will be no use of military in this,” Mr. Kelly said at a news conference on Thursday, appearing with Rex W. Tillerson, the secretary of state. “At least half of you try to get that right, because it continues to come up in your reporting.”
United States relations with Mexico have sunk to their lowest point in decades, with a steady stream of policy announcements and statements from the White House that have enraged the Mexican public and left their leaders scrambling to figure out how to respond.
But it remains unclear which version of Washington will come to bear on Mexico in the coming months —the more aggressive approach of the American president or the more reassuring stance of Mr. Tillerson and Mr. Kelly, whose job will be to oversee many proposals likely to antagonize Mexico the most.
“Let me be very, very clear,” Mr. Kelly added, assuring Mexicans that the rules for deporting people from the United States had not fundamentally changed. “There will be no, repeat no, mass deportations.”
The American visit to Mexico did little to resolve the differences and contradictions. Four officials — two from Mexico and two from the United States — walked into a large ballroom with grim faces and delivered carefully worded statements without taking questions.
It was the kind of cautious staging normally seen after tough negotiations between adversaries, not conversations between friendly neighbors. No one suggested that a breakthrough had been made.
“Two strong, vibrant countries from time to time will have differences,” Mr. Tillerson said.
The Mexican foreign minister, Luis Videgaray, made clear that some of the Trump administration’s orders, including the idea of shipping immigrants from other countries to Mexico, were not welcome.
“We’ve also talked about the legal impossibility of one government taking positions in a unilateral fashion that will affect another government,” Mr. Videgaray said.
In the last month, Mexican officials have often shown cautious restraint — or even remained silent — in response to Mr. Trump’s provocative policies and promises to build a border wall, often to the frustration of the Mexican people, who are hungry for a visceral reaction.
Their logic, officials say, is cleareyed: to descend into a fight with the United States would serve no one, least of all the Mexican people who so desperately want it.
But that is not to say they are without recourse in the event of a meltdown. From trade to security to migration, the Mexicans could severely damage United States interests and security if their hand is forced, experts say. And while they hope to avoid any such confrontation, the whispers of discontent have started to spread.
The economic minister has said there will be no trade discussions without talk of security of migration, twin areas of vulnerability for the United States. A congressman has submitted legislation that would divert Mexico’s billions of dollars in corn purchases from American farmers to other, more friendly neighbors. And the foreign minister, responding to an executive order from Mr. Trump broadening the scope of deportations in America, has vowed to take any such actions that violate human rights to the United Nations.
While no concrete actions have been taken, Mexico is keenly aware of its side of the double-edged sword when it comes to the bilateral relationship: Billions of dollars in agricultural purchases, a decade of security cooperation to dismantle cartels and intercept drugs destined for the United States, and the detention of hundreds of thousands of migrants traveling through Mexico on their way to America’s southern border.