O'Rourke said Trump's words and actions have consequences, and referred to one of the president's recent rallies. Local news reports said Saturday was a "tax-free shopping day", drawing thousands of shoppers to the mall looking for back-to-school deals.
Two of the patients who arrived at the hospital were children with non-life threatening injuries, he said. City police said on Twitter they had received "multi reports of multipe shooters".
Last Sunday a 19-year-old gunman opened fire at a food festival in northern California, killing three, including two children.
Ryan Mielke, a spokesman for University Medical Center of El Paso, said 12 people were brought to the hospital with injuries, including one that died.
"We don't want to do anything prematurely until we have accurate facts for you", Sergeant Robert Gomez said, declining to provide details on the injured.
"Our hearts go out to the victims of this horrific shooting and to the entire community in this time of loss", the governor said.
Texas Gov. Greg Abbott called the shooting "a heinous and senseless act of violence" and said the state had deployed a number of law enforcement officers to the city.
Police tape strung across an intersection behind the scene of a shooting at a shopping mall in El Paso, Texas, on Saturday, Aug. 3, 2019.
The shooting took place in El Paso, Texas, a city of about 683,000.
Vice President Mike Pence also expressed his condolences and said he was "grateful for the courageous efforts and swift action by federal law enforcement and local first responders".
Saturday's suspect was officially identified as a 21-year-old white male from Allen, Texas, a Dallas suburb some 650 miles (1,046 km) east of El Paso, which lies along the Rio Grande, across the U.S. -Mexico border from Ciudad Juarez. "We pray that God can be with those who have been harmed in any way and bind up their wounds".
Democratic presidential candidate Beto O'Rourke has abandoned a campaign event in Las Vegas to return to his hometown of El Paso.
El Paso has become a focal point of the immigration debate, drawing Trump in February to argue that walling off the southern border would make the US safer, while city residents and O'Rourke led thousands on a protest march past the barrier of barbed wire-topped fencing and towering metal slats.
"The perpetrator is not from El Paso and I do not believe anybody from El Paso would have done anything like this", he said. "The state of Texas and the Department of Public Safety are assisting the El Paso Police Department as they conduct their investigation".
"You could hear the pops, one right after another and at that point as I was turning, I saw a lady, seemed she was coming out of Walmart, headed to her auto".