The suspect eventually was killed by a bomb that authorities detonated, Brown said.
"We saw no other option but to use our bomb robot and place a device on its extension for it to detonate where the suspect was," Brown said.
"Other options would have exposed our officers to grave danger. The suspect is deceased as a result of detonating the bomb."
Five police officers were killed and seven others were injured in the ambush in Dallas that began Thursday night, officials have said, in the deadliest single incident for U.S. law enforcement since September 11, 2001. Two civilians also were injured in the shootings, the office of Dallas' mayor has said.
Most of the injured Dallas police officers have been released from a hospital, Brown told reporters. The officers' conditions are improving, Brown said.
"All I know is that this must stop -- this divisiveness between our police and our citizens," Brown said. "We don't feel much support most days. Let's not make today most days. Please, we need your support to be able to protect you from men like these, who carried out this tragic, tragic event."
Brown said an investigation into the ambush continues.
"I'm not going to be satisfied until we've turned over every stone. We've got some level that this one suspect did do some of the shooting. But we're not satisfied that we've exhausted every lead," he said. "So if there's someone out there who's associated with this, we will find you, we will prosecute you, and we will bring you to justice."
Shooters killed five officers during protests against police in downtown Dallas, marking the deadliest incident for U.S. law enforcement since September 11, 2001.
The gunfire started Thursday night as demonstrators marched against the shooting deaths of two African-American men by police in Louisiana and Minnesota.
A total of 11 officers were shot, and some of the six officers injured are undergoing surgery, authorities said.
It was the deadliest single attack on law enforcement since the 2001 terror attacks, when 72 officers died, according to the National Law Enforcement Officers Memorial Fund.
Here's what we know:
-- A total of 10 police officers were shot by snipers during the protests, Dallas Police Chief David Brown said. An 11th officer was shot during an exchange of gunfire with a suspect, authorities said.
-- Brown said it's unclear how many suspects were involved, but three people are in custody.
-- Dallas police negotiated and exchanged gunfire with a suspect for hours at a parking garage in downtown. That suspect is dead, a law enforcement official told CNN. The official did not say how the suspect died.
-- "The suspect told our negotiators that the end is coming," Brown said. The suspect at the garage also told negotiators more officers are going to get hurt, and that bombs are planted all over downtown Dallas.
-- Police found no explosives during primary and secondary sweeps of the area, Dallas police Maj. Max Geron said Friday morning on Twitter.
-- Two of the shooters were snipers, who fired "ambush-style" from an "elevated position," Brown said.
-- Officers killed include one DART officer. DART, the Dallas Area Rapid Transit agency, operates buses and commuter rail in the city and surrounding suburbs.
-- DART identified the officer killed as Brent Thompson, 43. He joined the transit agency in 2009, and was its first officer killed in the line of duty, DART tweeted.
-- Thompson got married just two weeks ago to a fellow transit officer, DART Police Chief James Spiller told CNN's "New Day" on Friday.
-- Witness Ismael Dejesus said he filmed the shooter from his hotel balcony about 50 yards away. He described the gunman as carrying a weapon with a "pretty big magazine."
-- Retired FBI special agent Steve Moore said an attack of that magnitude required advance work.
-- "This was an attack planned long before -- waiting for an opportunity to go," Moore said. "I think there was so much logistically, ammunition-wise. They may not have planned the location, they may not have planned the vantage point. But they had prepared for an attack before last night's shooting is my guess."
-- President Barack Obama, who is in Warsaw, Poland, said his team is keeping him updated. "We still don't know all the facts, we do know there's been a vicious, calculated and despicable act on law enforcement," Obama said. "I believe I speak for every American when I say we are horrified."
Peaceful protest shattered
Witnesses said the protesters were marching peacefully when the gunfire started. Crowds scattered.
"In the midst of it, gunshots just started barreling out," witness Michael Jackson told CNN's Don Lemon. "I immediately started running the opposite way."
G.J. McCarthy said he thought it was fireworks at first. The bangs got louder, and protesters realized it was gunfire.
"That went on for a while," he said. Crowds ran into a parking garage, and spilled out after word spread that there was a sniper nearby.
Clarissa Myles was eating at a McDonald's nearby when peaceful protests suddenly turned chaotic.
"Everyone was screaming, people were running," she said. "I saw at least probably 30 shots go off."
Two killings in two days
The shootings occurred as Americans nationwide took to the streets to demand answers over the killings of two black men in two days. They wept, marched and chanted "Black Lives Matter!"
In St. Paul, Minnesota, crowds gathered near the spot where an officer killed Philando Castile in a car on Wednesday.
"We are targets," LaRhonda Talley said in an impassioned speech in Minnesota. "We made it across the transatlantic. We made it to freedom and you're still killing us. You're still hanging us from trees. You're still killing us. Our lives matter! My son's life matters. He matters to me ... just like everybody's son matters to their mama."
Hundreds of miles away, more protesters marched outside a convenience store in Baton Rouge, Louisiana, where Alton Sterling was fatally shot Tuesday while police tackled him in a parking lot.
As has become a horrible norm, both killings were captured on video and posted online.
In Minnesota, the shooting of Castile was remarkable -- and heartbreaking -- because his fiancee live-streamed the immediate aftermath.
As her 4-year-old sat in the backseat, Diamond Reynolds calmly narrated what was going on and showed viewers the dying man groaning and bleeding in the front seat.
Castile, a school food services worker, was shot in Falcon Heights, outside Minneapolis, when a police officer pulled him over because of a broken taillight, said his fiancee, who was in the car with him.
"He let the officer know that he had a firearm and he was reaching for his wallet and the officer just shot him in his arm," Reynolds said as she broadcast the Wednesday shooting on Facebook.
"Oh God, please don't tell me my boyfriend is dead," she said.
Baton Rouge shooting
Sterling, 37, was killed Tuesday near a convenience store in Baton Rouge, where he regularly sold CDs and DVDs.
A homeless man approached Sterling on Tuesday and asked for money, becoming so persistent that Sterling showed him his gun, a source told CNN.
The homeless man called 911 and police arrived at the store. Police tackled Sterling to the ground, and shot him several times, video shows.
A law enforcement source told CNN that the officers pulled a gun from Sterling's body at the scene. No further details were provided on the type of firearm.
The convenience store quickly became the site of protests. Flowers and signs piled up in a makeshift memorial. Protesters chanted "Hands up, don't shoot," the line made famous in the Michael Brown shooting in Ferguson, Missouri, about two years ago. Brown was also shot by a police officer.
Most major cities, including Chicago and New York, held protests against police shootings Thursday night.