A US army veteran killed after five police officers were shot dead during a protest march in Dallas told authorities he was upset about the police killings of two black men earlier this week and wanted to exterminate white people, "especially white officers".

The man identified as 25-year-old Micah Johnson was killed by a robot-delivered bomb after the shootings, which marked the deadliest day for US law enforcement since the September 11 2001 terrorist attacks. A total of 12 officers were shot.

Johnson was a private first class from the Dallas suburb of Mesquite with a speciality in carpentry and masonry. He served in the Army Reserve for six years starting in 2009 and did one tour in Afghanistan from November 2013 to July 2014, the military said.

After the attack, he tried to take refuge in a parking garage and exchanged gunfire with police, Police Chief David Brown said.

But before his death, he described his motive during negotiations and said he acted alone and was not affiliated with any groups.

Mr Brown blamed "snipers" for Thursday's attack, but it was unclear how many were involved. Authorities initially said three suspects were in custody and the fourth dead.

The bloodshed unfolded just a few streets away from where President John F Kennedy was assassinated in 1963.

The shooting began on Thursday evening while hundreds of people were gathered to protest the killings in Baton Rouge, Louisiana, and suburban St Paul, Minnesota. Mr Brown told reporters that snipers fired "ambush-style" on the officers. Two civilians also were hurt.

Authorities said they were not sure they had located all possible suspects, but attention on Friday quickly turned to the man killed in the parking garage. A Texas law enforcement official identified him as Johnson.

Around midday, investigators were seen walking in and out of a home believed to be Johnson's in Mesquite.

None of the other suspects were identified, and the police chief said he would not disclose any details about them until authorities were sure everyone involved was in custody.

The nation's top law enforcement official, attorney general Loretta Lynch, called for calm, saying the recent violence cannot be allowed to "precipitate a new normal".

Ms Lynch said protesters concerned about killings by police should not be discouraged "by those who use your lawful actions as a cover for their heinous violence".

It appeared the snipers "planned to injure and kill as many officers as they could," Mr Brown said.

Video from the scene showed protesters marching along a street about half a mile from the City Hall when shots erupted and the crowd scattered. Officers crouched beside vehicles, armoured SWAT team vehicles arrived and a helicopter hovered overhead.

Demonstrations were held in several other US cities on Thursday night to protest against the police killings of two more black men. A Minnesota police officer fatally shot Philando Castile on Wednesday while he was in a car with a woman and a child, and the shooting's aftermath was livestreamed in a widely shared Facebook video. A day earlier, Alton Sterling was shot in Louisiana after being pinned to the pavement by two white officers. That, too, was captured on a mobile phone video.

The Dallas shootings occurred in an area of hotels, restaurants, businesses and some residential apartments only a few blocks from Dealey Plaza, the landmark made famous by the Kennedy assassination.

The scene was chaotic, with officers with automatic rifles on the street corners.

"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."

Local resident Carlos Harris told the newspaper that the gunmen "were strategic". He said: "It was tap, tap, pause. Tap, tap, pause."

Video posted on social media appeared to show a gunman at ground level exchanging fire with a police officer who was then felled.

Mayor Mike Rawlings said one of wounded officers had a bullet go through his leg as three members of his squad were fatally shot around him.

"He felt that people don't understand the danger of dealing with a protest," said Mr Rawlings, who spoke to the surviving officer.

"And that's what I learned from this. We care so much about people protesting, and I think it's their rights. But how we handle it can do a lot of things. One of the things it can do is put our police officers in harm's way, and we have to be very careful about doing that."

Four of the dead were with the Dallas Police Department. One was a Dallas Area Rapid Transit officer. The agency said that 43-year-old officer Brent Thompson, a newlywed whose bride also works for the police force, was the first officer killed in the line of duty since the agency formed a police department in 1989.

Theresa Williams said one of the wounded civilians was her sister, 37-year-old Shetamia Taylor, who was shot in the right calf. She threw herself over her four sons, aged 12 to 17, when the shooting began.

Other protests across the US on Thursday were peaceful, including in New York, Atlanta, Chicago and Philadelphia. In Minnesota, where Mr Castile was shot, hundreds of protesters marched in the rain from a vigil to the governor's official residence.

US President Barack Obama said America is "horrified" by the shootings, which have no possible justification. He called them "vicious, calculated and despicable".

Speaking from Warsaw, Poland, where he was meeting with leaders of the European Union and attending a Nato summit, the president asked all Americans to pray for the fallen officers and their families.

AP