"We do not agree on the different measures that recently were stated by the government of the United States (that) affect Mexico," Osorio Chong said.

Department of Homeland Security Secretary John Kelly and Secretary of State Rex Tillerson were in Mexico to try to smooth the relationship and address some of the differences that have emerged between the United States and its neighbor.

Their visit to Mexico City follows months of charged rhetoric from President Donald Trump and US immigration measures announced this week that have dramatic implications for the country, including potentially sending significantly more migrants back over the southern border.

"We have expressed our concern about the increase of deportations," Osorio Chong said of meetings he and other Mexican officials had Thursday with Kelly and Tillerson.

Mexican Foreign Minister Luis Videgaray, speaking ahead of Osorio Chong, was also quick to raise some of these tensions, telling reporters that there was a perception in Mexico that the Trump administration was pursuing "policies that might be hurtful for Mexicans."

Pointing to the issue of illegal migration, he said, "Our concern, to respect the rights of Mexicans living in the United States more, specifically the human rights."

He added that it would be "a long way to go" to be in agreement with the United States and that "facts" were needed in order to "overcome the negative feelings that are prevailing now."

Tillerson, for his part, noted that "two sovereign countries from time to time will have differences."

Standing with Videgaray, however, he focused more on shared concerns in his public comments.

"We listened closely and carefully to each other as we respectfully and patiently raised our respective concerns," he said.

"There's no mistaking that the rule of law matters on both sides of our border," Tillerson said, pledging to work with Mexico to stem the flow of cash and weapons from the US.

But his message in meetings, according to a senior administration official speaking after the top US diplomat's arrival in Mexico Wednesday night, was a little more forceful.

"Tillerson will make, he will acknowledge this, that if we are gonna to have a relationship that works, on border that works, it goes both ways," the official said.

Ahead of their remarks, President Donald Trump said Thursday that he told Tillerson the visit to Mexico was "going to be a tough trip."

Trump, speaking to manufacturers at the White House, said the trip would be difficult "because we have to be treated fairly by Mexico."

As Tillerson arrived Wednesday, Videgaray said publicly that he wanted to "make it clear, in the most emphatic way, that the Mexican government and the people of Mexico do not have to accept measures unilaterally imposed on a government by another government."

US administration officials said Kelly and Tillerson's trip was meant to allow the new Cabinet secretaries to establish relationships and coordinate on bilateral issues that range from counterterrorism, border security and trade amounting to $1.5 billion a day.

They also met with President Enrique Peña Nieto and Mexican military officials.

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But the top US officials make their Mexican debut under a cloud, as Trump has introduced policies meant to back up campaign rhetoric that painted Mexico and Mexicans as a security threat and economic drain on the US.

On Tuesday, the Trump administration issued guidance that broadens the scope of deportations from a previous focus on criminals to apply to every undocumented immigrant in the US. It also enables state and local law enforcement to act as immigration officers.

Another change to asylum procedures would make it easier for immigration officers to send non-Mexican migrants to Mexico if they came through the country on their way to the US. The change could potentially send tens of thousands of Central Americans fleeing violence, gangs and drug cartels back into Mexico.

A Mexican official, speaking on condition of anonymity to discuss sensitive diplomatic matters ahead of Thursday's meeting, told CNN that Kelly and Tillerson would hear from Pena Nieto, Videgaray and other officials that Mexico would not take deportees who are not Mexican nationals. A second official pointed out that no bilateral agreement requires Mexico to take these immigrants and that Mexico isn't bound by any US presidential order. There is nothing the US can't do to force the matter, this official said.

And Mexico has some leverage, the second official said. The country has been stopping Central American migrants before they reach the US for more than two years, the official said, adding that if Trump doesn't stop his "orders," it will make it more difficult for Mexico to continue this cooperation.

Trump may be trying to figure out his own ways to apply pressure to get Mexico to pay. He has suggested putting a 20% tariff on Mexican goods entering the US and his campaign has floated the idea of seizing remittances from Mexicans in the US sending money home.

The President has also ordered Cabinet agencies to inform him of the total direct and indirect aid the US gives Mexico, a move that some see as an attempt to amass some leverage in the debate over the border wall that Trump insists will be built and that Mexico will pay for. Mexican officials have repeatedly said they will do no such thing.

Under the Merida Initiative, the State Dept has given Mexico $2.6 billion since 2008. That's to strengthen rule of law, counter narco-trafficking, support judicial reform and police professionalization. It doesn't include aid from other State Department programs. Mexico also gets funding from the departments of Defense, Energy, Labor, Health and Human Services, Interior, the Peace Corps, the US Agency for International Development and DHS.

Kelly distributed an implementation memo on February 21 asking his staff to calculate how much direct and indirect aid DHS gives Mexico. That process is still underway.