The city of Dallas was in chaos in the early hours of Friday as police were hunting suspects after four officers were shot dead during a rally over the recent shootings of black men by police.

"It appears that two snipers shot 10 police officers from elevated positions during the protest rally," Dallas Police Chief David Brown said in a statement quoted by NBC 5.

Three of the fatalities were members of Dallas police, while the fourth was a security official with the local DART transport authorities, the report said.

An 11th officer was injured around 11 pm (0400 GMT) in a shootout with a suspect, it cited Brown as saying later.

Three suspects have been arrested, including a woman, Brown told a press conference early Friday.

Police put out a picture of a "person of interest," showing a man wearing a camouflage pattern shirt and appearing to carry a rifle. The man had handed himself in to police, and a relative had said he was a peaceful protester, the LA Times reported.

Two suspects were pulled over after driving away from the town centre in a black Mercedes at high speed, and were being questioned on suspicion of threatening to plant a bomb, Brown was quoted as saying in the report.

A fourth was holed up on the second storey of a car park at a shopping centre, negotiating and exchanging gunfire with police, Brown told reporters early Friday morning.

The suspect had warned that bombs were planted around the city, he said.

Local witnesses reported an explosion in the car park. "Seconds ago, [Dallas police] told us to move," local journalist Robert Wilonsky tweeted from his personal account around 1:30 am. "Then, a loud boom and what sounded like shattering glass."

The firing started around 9 pm in the city centre, the NBC report said.

The rally was to protest two killings of black men at the hands of police officers this week.

Philando Castile, 32, was shot late Wednesday near Minneapolis, Minnesota, as he tried to get out his wallet after being pulled over for a broken tail light, police said.

Alton Sterling, 37, was shot Tuesday by police in Baton Rouge, Louisiana, after officers responded to a complaint about a black male selling CDs and threatening the caller with a gun.

The US Justice Department said it was monitoring the state investigation into Castile's killing, and would hold its own into Sterling's death.

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