Five police officers were killed and seven wounded in a hail of gunfire during a protest on Thursday against the shooting of black men by police.
The suspect, 25-year-old Micah Johnson, died after a long stand-off with police in central Dallas.
Mayor Mike Rawlings said officials believed he was "the lone shooter".
"We believe now the city is safe," the city mayor said at a news conference on Friday.
The protest in Dallas took place after this week's deaths of Philando Castile in Minnesota and Alton Sterling in Louisiana.
Officials said on Friday that gunmen targeted police officers and civilians in separate attacks in Georgia, Missouri and Tennessee in the aftermath of the Minnesota and Louisiana deaths.
In Tennessee, a black army veteran killed a woman and also injured three other people, including a police officer, as he opened fire on a motorway on Thursday morning.
After his arrest, he told investigators he was troubled by police violence against African-Americans.
In the Georgian state capital Atlanta on Friday evening, thousands marched in protest at the recent police shootings.
The protesters are currently in a stand-off with police as they block a major road