The 25-year-old army vet opened fire with a powerful rifle during a peaceful protest Thursday evening in Dallas against the shooting deaths just days earlier of two black men, in Louisiana and Minnesota.
Officers searched the garage after using a shotgun to break a lock on a fence there, but the hunt turned up nothing.
After shooting at the Dallas officers, Johnson tried to take refuge in a parking garage and exchanged gunfire with police, authorities said.
According to an internal police memo obtained by Eyewitness News, a group from Houston was allegedly driving to Dallas with the intent of killing more police officers.
"If this had not been a crime of opportunity where the protest was quickly organized in response to events in the same week... he could have caused a lot more harm than he did", Jenkins said.
Two patrol cars serving as a memorial outside of police headquarters were adorned with flowers, signs and flags by some of the people pausing to pay their respects to the five officers killed and seven wounded.
The department is taking extra safety precautions, it said in a statement.
A city-wide roll call has been started by officers to check on the welfare of all Dallas police officers.
President Barack Obama on Saturday rejected any notion that the past week's stunning violence signals a return to racial brutality of a dark past, saying that as painful as the killings of police and black men were, "America is not as divided as some have suggested". "Obama has come out and addressed the nation, sent a message to his people, and said 'We haven't been able to beat this, I'm very upset.' Even for a powerful country, I guess it means that America has not yet been able to overcome this thing called racism'".
During negotiations, he said he wanted to exterminate whites, "especially white officers", the police chief said.
And at Dallas' Cathedral Shrine of the Virgin of Guadalupe, Roman Catholic parishioners gathered on Sunday for their weekly service and to remember the fallen officers.
"I would like you to join me in asking: 'Who is my neighbour?'" Rev Eugene Azorji, who is black, told the congregation. "Those who put their lives on the line every day to bring a security and peace, they represent our neighbour".
Dallas police said they searched for a suspicious person in a parking garage next to its headquarters, but that no suspect was found, CBS2's Kenneth Craig reported.
A candlelight vigil is set for 8 p.m. on Monday in Dallas City Hall plaza.