Here are the 10 latest developments in this story:
The attack, one of the worst mass police shootings in US history, happened during a protest against the killing of two black men by police in Louisiana and Minnesota this week.
According to the police, one of the suspects is a woman. Two others were taken into custody as they tried to flee in a car.
The fourth suspect - who was holed up in a downtown garage - had told negotiators that the "end is coming" and that "there are bombs all over the place in this garage and in downtown." Police sources say he has been killed.
US aviation authorities restricted flights over Dallas soon after five police officers were fatally shot and six others were injured by snipers who shot from rooftops.
The police said it appeared to be a coordinated attack. Dallas Police Chief David Brown told reporters the snipers fired "ambush style" upon the officers.
The gunfire broke out around 8:45 pm local time. Local media reports showed protesters marching along a street in downtown when the shots erupted and the crowd scattered, seeking cover.
Soon after the shooting was reported, police released a photo of one of the suspects. Minutes later, it tweeted to say "the person of interest whose picture has been circulated just turned himself in".
But the brother of the man whose picture was released claimed that he was innocent. Some reports now say he has been released, but there is no official word from the police on it yet.
President Barack Obama, visiting Poland, was briefed about the shooting that he termed "vicious, despicable and calculated attack."
The Dallas-Fort Worth metropolitan area is one of the nation's most populous and is home to more than 7 million people.
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