The statements by Videgaray and Interior Minister Miguel Angel Osorio Chong, who minimized the potential impact of the rumored loss of US security aid, toughened the defiant tone from Mexico since President Enrique Pena Nieto last month canceled a trip to meet Trump over the wall dispute.
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 almost a dozen states to help enforce immigration laws.
But it is unclear whether the USA has authority to force Mexico to accept foreigners.
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.
"We agreed that our two countries should seize the opportunity to modernize and strengthen our trade and energy relationship", he said.
Kelly and Tillerson assured Mexican officials that the U.S. would continue to cooperate with them on border issues, though Mexican officials were expressing growing concerns about Trump's apparent intention to act unilaterally. Both diplomats said, although acknowledging the fraught relations, that directly discussing their differences was in their shared interests.
Trump portrayed the immigrants targeted as criminals.
On Tuesday, the Department of Homeland Security released new guidelines for deportations that prioritize undocumented immigrants with any criminal offense, broadening the group that can be targeted, according toThe Hill.
But would it actually be illegal for Trump to use the military or the national guard for deportations?
Mexico has hinted it could use border cooperation as a bargaining chip.
Mexico's Interior Minister Miguel Osorio Chong expressed disagreement Thursday "with some of the measures announced by the USA government that have implications for our country and compatriots".
The main US aid to Mexico is under the Plan Merida programme which allocated $2.6 billion (£2 billion) to security assistance.
In fact, they used Thursday's meeting to express "concern about the increase of deportations", Osorio Chong said.
While he voiced concern for all immigrants who could be affected, Bishop Vasquez said it was particularly worrisome that the memos seem to "eliminate important protections for vulnerable populations, including unaccompanied children and asylum seekers" and "greatly expand the militarization of the U.S. -Mexico border".
Donald Trump declared during a White House meeting that there was a "military operation" underway to deport undocumented American immigrants.
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