Interior Minister Francisco Rivas yesterday said he and Kelly discussed those issues after the US official, who arrived late Tuesday, held private talks with Guatemalan President Jimmy Morales.
Journalists were not permitted to photograph the meeting with Morales, whose office instead provided some images. The officials did not hold a press conference.
Rivas said his talks with the Homeland Security chief revolved around migration and "criminal entities that affect both countries," such as drug cartels and violent gangs active in Central America.
US President Donald Trump's calls to reduce migration and deport some of the estimated 11 million undocumented immigrants in the United States has unsettled Central American countries, from which many of the migrants hail.
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Kelly issued tough new orders Tuesday for a sweeping crackdown on illegal immigrants in the United States.
In one of two memos issued, he said: "The surge of illegal immigration at the southern border has overwhelmed federal agencies and resources and has created a significant national security vulnerability to the United States."
Today Kelly and Trump's secretary of state, Rex Tillerson, will go to Mexico to meet with President Enrique Pena Nieto.
Trump has angered Mexico by vowing to build a wall to keep out migrants from Latin America and revise trade relations. During his election campaign, Trump branded some immigrants from Mexico as rapists and criminals.