The first victim to be named was that of Dart (Dallas Area Rapid Transit) Officer Brent Thompson. Dart tweeted:
"DART grieving the loss of Ofc Brent Thompson, 43, killed during Thurs protest. First DART officer killed in line of duty. Joined DART 2009."
Earlier, police tweeted a picture of a suspect asking for the public's help. The man pictured handed himself in and has since been released.
A fourth suspect who was involved in a shootout with police has killed himself, local media reports.
The suspect told police that "the end is coming" before shooting himself.
Dallas Police Department Chief David Brown said earlier, "The suspect we are negotiating with ... has told our negotiators that the end is coming and he's going to hurt and kill more of us ... and that there are bombs all over the place, here and downtown."
Police are now conducting extensive sweeps for explosives across Dallas downtown.
Brown believed four people had worked together to launch the attack, but he did not speculate on any motive for the shootings. He said the people in custody were not cooperating.
Brown said at least two snipers took "elevated" positions on downtown garages and "planned to injure and kill as many law enforcement officers as they could".
The police department have also issued a statement in relation to a chase on the freeway near downtown Dallas.
"Another alleged suspect was in a shootout with Dallas SWAT officers. That suspect is also in custody. A suspicious package was discovered near this suspect's location.
"A DPD officer observed an individual carrying a camouflaged bag, walking quickly down Lamar St. The individual threw the bag in the back of a black Mercedes and the Mercedes sped off at a high rate of speed.
Officers followed the vehicle southbound on l-35E and performed a traffic stop at i-35E and Kiest. Police are questioning both occupants of the vehicle."
"The package is being secured by DPD bomb squad."
There are reports that one of the transit officers who was shot and survived has been identified by her father as Misty McBride. He said his daughter has been a transit officer four about five years, and was wounded in the shoulder and abdomen.
According to the New York Post, broadcaster KABC reported that shots were fired at about 8:45pm during demonstrations at Belo Garden Park in Dallas. Footage showed a heavy police presence with officers taking cover behind vehicles on the street.
Fox News reports protestors were chanting "F**k the police" before the shooting.
It is believed the gunman was wearing "survival gear".
Live TV video showed protesters marching along a street when the shots erupted and the crowd scattered, seeking cover.
Scores of police and security officers were on hand. Police and others hunched behind cars outside a carpark. Officers with guns drawn were running near and into a carpark as police searched for the shooter.
"Oh my God, I mean we're all seeing this together," one reporter could be heard during a live cross.
"This is not clear, it is not clear, it's not clear to me what we are seeing but the situation is escalaiting. That officer is not moving."
A police dispatcher reached by The Associated Press had no immediate comment while a spokesman for the mayor said he had no information he could share.
Firefighters and police at the scene were keeping people away.
"Everyone just started running," Devante Odom, 21, told The Dallas Morning News.
"We lost touch with two of our friends just trying to get out of there." Carlos Harris, who lives downtown, told the newspaper that the shooters "were strategic".
"It was tap tap pause. Tap tap pause."
The protest was sparked after the deaths of two black men this week, including Philando Castile, who was killed on Wednesday (local time) during a traffic stop in Falcon Heights, a suburb of Minnesota.
His girlfriend, Diamond Reynolds, recorded the aftermath of the incident on live video. She said Castile was shot five times as he sat at the steering wheel reaching into his back pocket for his ID.
- nzherald.co.nz and agencies