"It's really a disgrace,"? St. Paul Police Chief Todd Axtell said.
The attacks have also clouded the future of Black Lives Matter, an anti-racism movement that has gained strength after the police killings of African-Americans but has also been criticized for vitriolic social media postings against police, some of them sympathetic to Johnson.
US President Barack Obama, speaking in Madrid as part of a European tour, warned that attacks on police over racial bias would hurt Black Lives Matter, saying there will always be people who make "stupid" or "overgeneralizing" comments.
"Whenever those of us who are concerned about failures of the criminal justice system attack police, you are doing a disservice to the cause," America's first black president told a news conference.
"I don't think you can hold well-meaning activists ... responsible for everything that's uttered at a protest," he said.
On Friday, the government of Bahamas warned its citizens to be careful when visiting US cities, offering the kind of advice, often referred to as "the talk," that black parents typically have with their teenage sons.
"Young males are asked to exercise extreme caution in affected cities in their interactions with the police. Do not be confrontational and cooperate," the Bahamas foreign ministry said in its travel advisory.
Police in Dallas were also questioned over their decision to use a bomb mounted on a robot to kill the gunman while he was holed up after killing the five officers.
INITIALS SCRAWLED IN BLOOD
Brown, the police chief, vigorously defended the tactic, saying he approved the plan to detonate a bomb with "about of pound" of C-4 explosives after two hours of fruitless talks with the suspect, who sang, laughed and taunted police negotiators.
Although police believe Johnson acted alone, "we still have not ruled out whether or not others were complicit," Brown said.
Brown also revealed in the CNN interview that Johnson wrote the letters "RB" in his own blood when engaged in a standoff with police, a mysterious clue that remains under investigation, the Dallas police chief said.
"He wrote some lettering in blood on the walls, which leads us to believe he was wounded on the way up the stairwell," Brown said, adding that police were trying to decipher what RB meant.