(Adds Pena Nieto, tequila at dinner)
By Alexandra Alper and Noe Torres
MEXICO CITY, Feb 23 (Reuters) - Mexico on Thursday expressed "worry and irritation" about U.S. policies to two of President Donald Trump's top envoys, giving a chilly reply to the new administration's hard line on immigration, trade and security.
Comments by Trump about a "military operation" to deport criminals added to the tense atmosphere, and prompted a clarification from Homeland Security chief John Kelly, one of the U.S. officials visiting Mexico City.
The U.S. government angered Mexico this week by saying it was seeking to deport many illegal immigrants to Mexico if they entered the United States from there, regardless of nationality.
It is the latest point of friction between neighbors that have also been at odds over Trump's vow to build a wall on the border and his attempts to browbeat Mexico into giving concessions on trade.
"There exists among Mexicans worry and irritation about what are perceived to be policies that could be harmful for the national interest and for Mexicans here and abroad," Foreign Minister Luis Videgaray told a news conference.
He was speaking after talks in the Mexican capital with U.S. Secretary of State Rex Tillerson and Kelly, who later met with President Enrique Pena Nieto. The Mexican leader scrapped a summit meeting with Trump in January as tensions rose.
Tillerson and Kelly emphasized traditionally strong U.S.-Mexico ties and both sides pledged further dialogue on migration, trade and security issues. Pena Nieto said the talks were a sign of the will to build a constructive relationship.
Two Mexican newspapers leaked comments from Videgaray, however, that bolstered the perception that Mexico is taking a more robust approach to its dealings with Trump, following jibes that Pena Nieto should stand up to his counterpart.
If the United States taxes imports from Mexico, there will be a response that "hits them where it hurts," La Jornada and Reforma reported Videgaray as saying, based on recordings obtained of a closed-door session with lawmakers on Wednesday.
Videgaray warned of counter-taxes and tariffs targeting U.S. congressional districts most reliant on exports to Mexico if Trump started limiting trade.
Kelly and Tillerson were more measured in their words than either the Mexicans or Trump, who said on Thursday a military operation was being carried out to clear "bad dudes" such as gang members and drug lords from the United States.
Kelly said there would be "no use of military force in immigration operations," and "no, repeat, no" mass deportations. White House spokesman Sean Spicer said Trump's comment was meant to describe the "flawless" manner that U.S. immigration and border authorities worked.