The shopping center where the terror attack took place is in close proximity to the US-Mexican border.
Allen, the El Paso police chief, said the gun used in the attack was legally purchased near Crusius' hometown.
Travelers are urged to take precautions 'in the face of growing indiscriminate violence, mostly for hate crimes, including racism and discrimination, which cost the lives of more than 250 people in the first seven months of this year, ' it said in the release also posted on President Tabare Vazquez's website. "The situation, needless to say, is a horrific one".
Patrick Crusius, 21, of Allen, Texas, a Dallas suburb more than 600 miles from El Paso, is the suspect, a law enforcement source with direct knowledge of the investigation tells PEOPLE. Authorities have now brought capital murder charges against him.
In his speech, the president claimed that before the construction of the wall between the two cities between 2008-09, El Paso was considered "one of our nation's most risky cities" for its "extremely high" rate of violence, a statement that was easily proven to be false.
El Paso police said Monday that one of the victims in the Walmart attack was a German citizen. "I don't know how we deal with evil. It will leave an impression that you'll never forget".
Travel warnings were mirrored by stunned global coverage of the two shootings, which took place within 13 hours of one another and in which both gunmen used high-capacity magazines and military-style semi-automatic weapons, which are legal in the states where the gunmen bought them.
Police say some of the dead are being returned to family members.
Crusius, of Allen, Texas, has been jailed without bond.
Still, some, like Ernesto Carrillo, whose brother-in-law Ivan Manzano was killed in the Walmart attack, said the president shares blame for inflammatory language Carrillo called a "campaign of terror".
"I will continue to challenge any harmful or inaccurate statements made about El Paso", Margo said. Years of drug violence in neighboring Ciudad Juarez, Mexico, left tens of thousands of people dead, yet El Paso had one of the nation's lowest crime rates.
Earlier on Monday, Trump said that the El Paso gunman was "consumed with racist hate" and asserted that "hate has no place" in his country.
Texas Governor Greg Abbott said Saturday's rampage in the heavily Hispanic city appeared to be a hate crime, and police cited a manifesto they attributed to the suspect as evidence that the bloodshed was racially motivated.
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