Patrick, the second-highest ranking elected official in Texas, blamed the attack on Black Lives Matter protesters and "people on social media, with their hatred toward police".
Witnesses said shots rang out as the protest in Dallas was winding down, sending marchers screaming and running in panic through the city's streets.
This week's killings of two black men by police officers in Louisiana and Minnesota were the latest in a long string of similar, controversial killings that have led to nearly two years of national protests over race and justice.
The Dublin-born Bishop of Dallas Kevin Farrell said last night that the killings were "a symptom" of the heightened political rhetoric and increasing polarisation in U.S. society.
"This was a well-planned, well-thought-out, evil tragedy by these suspects".
A person of interest whose photo was distributed by police has turned himself in, the department said.
Turner said the actions of one or two people can not cause people to stigmatize certain groups, including police officers, as well as those who attacked them.
"The suspected stated we will eventually find the IEDs", Brown said. "He said he was upset with the recent police shootings", Brown said, describing the conversation between the suspect and negotiators.
Rawlings said Micah Xavier Johnson, 25, was "the lone gunman in this incident". Details on how the shootings unfolded remained unclear. One video showed a gunfight with a suspect shooting an officer at point-blank range as he lay on the ground.
So Friday, he broke away from a North Atlantic Treaty Organisation summit in Warsaw and faced the cameras again to condemn the "vicious, calculated and despicable attack" in Dallas.
Two law enforcement officials told NPR's Dina Temple-Raston that they believe the suspect had been planning an attack for some time and acted on his own. The killings have spurred nearly two years of periodic and largely peaceful street protests.
"If there's someone out there that was associated with this, we will find you and we will prosecute you, and we will bring you to justice", Brown said.
He goes on to say that he will provide them with the best and safest tools and training to give them protection.
Earlier, there were reports of explosives set in the area where the standoff took place.
In all, eight Dallas police officers and four transit officers were wounded, along with a civilian in the gunfire about 8:45 p.m., police said. Police saw a man throw a camouflage bag in the vehicle.
"(I'm) exhausted of y'all tryin to be on these cops side making it okay based off irrelevant info when our own get killed over unjust s--", Nicole Johnson said on Wednesday. "We do not know who might have known what the gunman was going to do".
The Dallas attack marks the deadliest day for USA law enforcement officers since the 9/11 attacks in 2001. Three officers are deceased, two are in surgery and three are in critical condition.
Johnson lived in the Dallas suburb of Mesquite, according to United States media.
Bud Fox told reporters enough is enough.