Mexican leaders scolded their American counterparts on Thursday for President Trump’s new immigration policies, using an initial meeting to register their displeasure and demand that the U.S. not increase the number of people deported to Mexico.

The American leaders, Secretary of State Rex W. Tillerson and Homeland Security Secretary John F. Kelly, took the rebuke, promising to work with Mexico and vowing not to conduct “mass deportations” from within the U.S.

Mr. Kelly also took pains to rule out the possible use of military forces in immigration enforcement, pushing back on reports last week that the National Guard might be enlisted — and countering President Trump’s own description Thursday of his new deportation policies as “a military operation.”

“Listen to this: No, repeat, no use of military force in immigration operations. None,” Mr. Kelly said, pleading with reporters to “try to get that right” in their stories.

After a day’s worth of meetings in Mexico City, both sides emerged to say the talks were productive and cordial. But the encouraging words could not obscure the deep divisions that have emerged over trade and immigration policy early in the Trump administration.

The divides are so many that they didn’t even get to trade during this trip, Mexican Foreign Minister Luis Videgaray said through a translator.

Instead, he and Mexican Interior Minister Osorio Chong — seemingly responding to political demands within their own country — sounded defiant notes on immigration, saying they won’t allow the U.S. to unilaterally dictate deportation policies.

Mr. Chong said, through a translator, that his government had “expressed our concern of the increase of deportations and the possibility of citizens of other countries that could be returned or sent back to our territory.”

“We will insist [on] the need of maintaining the deportation schemes in an orderly fashion so as to guarantee the rights of all Mexicans in your country,” he said.

Mexican officials did concede that their country has become the transit route for illegal immigrants streaming from Central America to the U.S.

Indeed, Mexico often helps facilitate journeys of those trying to cross from its southern border to its northern border, where they prepare to try to gain entry to the U.S.

In one stark example, Mexico has been issuing temporary transit visas at its southern border to Haitians, giving them just long enough to reach the U.S. border, where they either try to sneak in or they show up at a border checkpoint and demand entry. More than 7,000 Haitians tried to claim entry in the last three months of 2016 alone — more than four times the previous pace.

Under Mr. Trump’s new policy, those Haitians and others who try to enter without permission would not only be put into faster deportation proceedings, but could even be shipped back to Mexico while they await the outcome of their court cases.

Mexico strenuously objected to that proposal and to the overall tenor of Mr. Trump’s policies, laid out in two Jan. 25 executive orders and then in memos from Mr. Kelly at Homeland Security this week.

“There’s a concern among Mexicans, there’s irritation before what has been perceived as policies that might be harmful for the Mexicans,” Foreign Minister Luis Videgaray said through a translator.

Mr. Trump has made things more difficult for his team through his own words and phrasing.

Last week Mr. Trump said a series of operations to find hundreds of illegal immigrants was the fruit of his executive orders — even though Homeland Security officials said they weren’t related.

And on Thursday Mr. Trump called the carrying out of his deportation policies “a military operation” that is getting “really bad dudes” out of the U.S.

“All of a sudden, for the first time, we’re getting gang members out,” Mr. Trump said. “What has been allowed to come into our country, when you see gang violence that you’ve read about like never before, much of that is people who are here illegally. And they’re rough and they’re tough, but they’re not tough like our people. So we’re getting them out.”

But his use of the word “military” renewed fears among activists who recalled a draft Homeland Security memo leaked last week that contemplated enlisting National Guard troops in nearly a dozen states to help enforce immigration laws.

Mr. Kelly shot that idea down, and White House press secretary Sean Spicer later said Mr. Trump was speaking descriptively, not literally, when he said “military operation.”

“The president was using that as an adjective. It’s being done with precision,” Mr. Spicer said. “The president was clearly describing the manner in which this is being done. It’s being done with a high degree of precision and in a flawless manner.”

• Dave Boyer contributed to this article.

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