"We're getting gang members out, we're getting drug lords out, we're getting really bad dudes out of this country - and at a rate that nobody's ever seen before," Trump told a group of manufacturing executives during a policy discussion.
But in Mexico, Kelly stated in response: "There will be no - repeat, no - use of military force in immigration operations. None."
White House press secretary Sean Spicer said Trump used "military operation" as an "adjective" to mean the level of precision of the immigration raids.
The meeting between the senior US and Mexican officials inside the Mexican Foreign Ministry struck a conciliatory tone, with both sides insisting that the day-to-day relations that include cooperative agreements on immigration, counterterrorism and trade amounting to US$1.5 billion ($2b) in daily commerce are too important to be derailed by political disagreements.
Tillerson said his conversations with Mexican officials were "forward-looking", with a long view of what is at stake for the two countries.
"In our meetings, we jointly acknowledged that, in a relationship filled with vibrant colours, two strong sovereign countries from time to time will have differences," Tillerson said in a prepared statement.
"We listened closely and carefully to each other as we respectfully and patiently raised our respective concerns."
The two sides said they agreed to work together through a combination of security and economic development initiatives to stem a heavy flow of illegal immigration into the US from violent areas of Central America.
Videgaray said both countries hope to lead a wider dialogue in the region that would add stability to Central America.
"We need to assume a regional responsibility for the development of Central America," he said.
Videgaray raised the Mexican Government's concerns about Trump's immigration order, which also directs US authorities to deport to Mexico all those who crossed the southern border illegally, even if they are not Mexican nationals.
"We have expressed to the secretaries, above all, our preoccupation over the rights of Mexicans in the United States, in particular human rights," he said.
But former Mexican President Vicente Fox said yesterday that the gestures by Tillerson and Kelly to smooth over relations shouldn't be taken seriously while Trump continues to talk about building a wall at the border and characterises Mexican immigrants as criminals.
"All he does is destroy, attack and offend while his people speak suavely about creating better relations," Fox said. "It's a big lie."
Analysts say the Trump Administration wants to show residents and business investors on both sides of the border that cooler heads will prevail in relations between the two countries.
"There's a lot at stake in the day-to-day cooperation between these two countries on security, migration and, above all, economics," said Andrew Selee, director of the Mexico Institute at the Woodrow Wilson Centre in Washington.
"Tillerson and Kelly are going to want to see how they can preserve a good day-to-day relationship with Mexico even if things get rocky politically."
In Mexico, Pena Nieto's critics urged him to take a tougher stand against a US President who they say cannot be trusted - after Trump signed an Executive Order to build a border wall on the eve of last month's scheduled White House visit and then signed the immigration enforcement order ahead of Tillerson and Kelly's visit to Mexico.
"This is worse than Lucy and Charlie Brown with the football," said Jorge Castaneda, who served as Mexico's Foreign Minister in Fox's Administration. "You'd have to be dumb to think that they're not going to do this again and again."
But Pena Nieto is in a delicate position as he looks to stabilise a struggling Mexican economy made more vulnerable by the uncertainty over US relations.
This week, he tried to prepare Mexico for a recalibrated relationship with its powerful northern neighbour that, among other things, could mean a new deal similar to the North American Free Trade Agreement, which Trump has called "the worst trade deal in history".
Pena Nieto's Government has been analysing potential bargaining points for renegotiating Nafta in the hopes of avoiding economic turmoil in a country where the peso has fallen in value.
In a meeting with Mexican media executives, Pena Nieto said Nafta may change in name only, according to the El Universal daily. But, he cautioned, relations with the Trump Administration are "a panorama of uncertainty", the newspaper reported.
