UPDATE 1-Mexico 'profoundly laments' U.S. move to end 'Dreamers' program

(Adds quote, details on government response, background on U.S.-Mexico relationship)

MEXICO CITY, Sept 5 (Reuters) - The Mexican government said on Tuesday it "profoundly laments" U.S. President Donald Trump's decision to phase out a popular program that shields hundreds of thousands of young unauthorized migrants from deportation.

The United States' southern neighbor will strengthen efforts to guarantee consular protections for affected Mexican youth, Mexico's Foreign Ministry said in a statement.

A majority of the nearly 800,000 young men and women who were brought into the United States illegally as children and protected under the Deferred Action for Childhood Arrivals (DACA) program are Mexican nationals, or some 625,000, according to Carlos Sada, Mexico's deputy foreign minister.

"They are exceptional. ... This is as emotional for the United States as for Mexico," he said at a news conference immediately following the announcement to end the program, urging for a quick solution to the uncertainty that "dreamers," as they are commonly called, now face in their adopted home.

Mexico will welcome migrants who opt to return to Mexico with "open arms," Sada said, offering assistance with work, finances and education.

The U.S. announcement to end DACA, created by former President Barack Obama in a 2012 executive order, came during the final day of talks in the Mexican capital to modernize the North American Free Trade Agreement, adding pressure to already tense conversations between the neighbors. (Additional reporting by Daina Beth Solomon, David Alire Garcia and Adriana Barrera; Editing by Paul Simao and Leslie Adler)