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Americans were grappling on Sunday with yet another mass shooting after a heavily armed man stormed a shopping mall in Texas, murdering eight people and wounding several others before he was killed by police.

Responders, distressed witnesses and police described scenes of panic and horror north of Dallas, where video footage circulating online showed the shooter getting out of a sedan in the outlet mall's parking lot on Saturday and opening fire on people walking nearby.

An officer inside on an unrelated call quickly responded to the gunfire and "neutralized" the shooter at the sprawling facility in Allen, police said.

The identity of the shooter was not released and no motive was put forward. The suspect's body, sprawled on a sidewalk, was one of seven deaths at the mall when more police arrived.

Two others died in the hospital while "three are in critical surgery, and four are stable", said Allen fire chief Jonathan Boyd.

US President Joe Biden, a proponent of stricter gun laws, released a proclamation on Sunday "as a mark of respect for the victims of the senseless acts of violence" in Allen.

It ordered US flags be lowered to half staff at the White House, public buildings and military facilities.

The attack is the latest in a shocking spate of deadly gun violence to convulse the United States.

Barely a week earlier, a man shot and killed five neighbours in Cleveland, Texas after one of them asked him to stop firing his rifle in his yard at night while a baby slept.

Awash in firearms, the country has already endured 199 mass shootings this year, according to the Gun Violence Archive, a non-governmental organisation which defines a mass shooting as four or more people wounded or killed.

The gunfire on Saturday at Allen Premium Outlets, 35 miles (55 kilometres) north of Dallas, began around 3:30pm (2030 GMT), when it was busy with weekend shoppers, police said.

The officer in the mall "heard gunshots, went to the gunshots, engaged the suspect and neutralized the suspect," said chief Brian Harvey of the Allen police department.

Some of the victims were as young as five, a hospital official told NBC News.

Texas Governor Greg Abbott called the mass shooting an "unspeakable tragedy".

But on Sunday, as Democrats repeated calls for Congress to enact gun safety legislation and blasted Texas and other states for allowing permitless carry.

Abbott, a Republican, refused to be drawn on whether restricting gun sales or enacting other reforms should be considered.

"People want a quick solution. The long-term solution is to address the mental health issue," he told Fox News on Sunday, saying the focus should be on growing "anger and violence" in America.

Local officials hailed the actions of the police officer who charged and killed the shooter.

"We owe a debt of gratitude to first responders that ran toward the gunfire and acted swiftly to neutralize the threat," said Keith Self, a Republican congressman whose district includes the city of Allen.

The police chief later said authorities believe the unidentified shooter "acted alone".

CNN showed a cropped photograph of the apparent gunman dead on the ground, wearing tactical gear with extra magazines, and with an AR-15-style rifle at his side.

'Unfathomable' carnage

Steven Spainhouer said he was confronted with haunting, unforgettably graphic images when he rushed to the scene and performed CPR on victims before the official first responders arrived.

Finding one female victim on the ground, "I felt for her pulse, pulled her head to the side, and she had no face," Spainhouer told CBS News.

He found the son of another victim lying under his dead mother and "covered head to toe" in blood.

"It's just unfathomable to see the carnage," he said.

Janet St. James, a spokesperson for Medical City Healthcare, which operates multiple trauma facilities in North Texas, said it received eight patients from the shooting, ranging in age from five to 61, NBC News reported.

"Allen is a proud and safe city which makes today's senseless act of violence even more shocking," mayor Ken Fulk said in a statement, as he said the quick response of authorities likely saved lives.

Jaynal Pervez, who arrived at the mall while his daughter was inside, told CNN: "There's no more safe places. I don't know what to do."

With more firearms than inhabitants, the United States has the highest rate of gun deaths of any developed country â€“ 49,000 in 2021, up from 45,000 the year before.