A man killed at least four people and wounded three others in an hours-long shooting rampage across Memphis on Wednesday, before a high-speed chase that ended with his arrest, police in the US city said.

Officers identified the suspect as Ezekiel Kelly, 19, and said he was apprehended with two weapons in his vehicle at approximately 9:00 pm local time (01:00 GMT on Thursday).

"(Kelly) was taken into custody without incident by the Memphis police department and the Shelby County sheriff's office," said Memphis police chief Cerelyn Davis at a news conference.

Kelly is alleged to have killed his first victim just after midnight on Wednesday, and gone on a shooting spree across the Tennessee city in the afternoon and early evening, Davis said.

There were at least eight different crime scenes, police said, including carjackings and a shooting at a local store, and Kelly had live-streamed parts of his spree.

"Ezekiel Kelly was on Facebook Live when he opened fire inside the store," said Davis.

Authorities issued a "shelter in place" order while the shootings were ongoing, effectively locking down parts of the city.

The United States regularly sees mass shootings and other gun violence, but Congress has been reluctant to pass strict gun control legislation as the issue remains politically divisive.

At least 490 people have been killed in mass shootings and mass murders in the US in 2022 so far, according to the Gun Violence Archive, with 14,050 people dying in gun-related incidents over the same period, excluding suicides.

Memphis has seen a string of high-profile killings in recent months, including the murder of a pastor during a carjacking and the abduction and murder last week of a woman who was on a pre-dawn run.

"I am angry. I am angry for (the victims) and I'm angry for our citizens who had to shelter in place for their own safety until this suspect was caught," said Memphis Mayor Jim Strickland following Wednesday's shootings.

"This is no way for us to live, and it is not acceptable."