During the interview, Brown added that there were indications Johnson was planning more wide-spread attacks, saying, "We're convinced this suspect had other plans and thought that what he was doing was righteous".
Five police officers were shot dead and seven others injured in "ambush style" firing by snipers in Dallas during a late night on demonstration protesting the fatal police shootings of black men on July 8, making it one of the deadliest days for police in USA law enforcement history.
He said 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 with police negotiators.
Chief David Brown said at the news conference that the Arlington Police Department has offered to work with the Secret Service to provide security during the president's visit.
The name of the group for which Johnson sought membership was not given, but The Daily Beast characterized the group as one of several Johnson was interested in that believes "in armed resistance against white society, especially police".
He has since seen the department through hard times, including a near riot after an officer-involved shooting and an attack on police headquarters.
Brown said he became increasingly concerned that "at a split second, he would charge us and take out many more before we would kill him".
Dallas police announced plans for the first three of the officers' funerals, which will take place tomorrow and Thursday.
Killing Johnson was "not an ethical dilemma", he said.
"He just basically lied to us, playing games, laughing at us, singing, asking how many did he get and that he wanted to kill some more", Brown said, according to USA Today.
City police said that Alva Braziel was carrying a gun, and was believed to have pointed it at officers, but in surveillance footage from a nearby gas station, he appears to put his hands up and turn around.
Police killed Johnson with a bomb-carrying robot, ending a standoff.
Johnson was killed by police who used a bomb detonating robot following negotiations.
"Bravery is not a strong enough word to describe what they did that day", Brown said of officers' response to Thursday's events.
Johnson was also a former US Army reservist, and indications suggest that he planned to use his combat training to launch more attacks beyond Dallas. "I'd do it again to save our officers lives".
"We are sworn to protect you and your right to protest, and we'll give our lives for it", he said.
"We're trying to figure out through looking at things in his home what those initials mean", the police chief said.
"We are sad, we are overwhelmed, we are in disbelief and yes, we are angry", said Senior officer Marcella St John, Michael Smith's longtime partner.
Amid the dizzying currents of protest and violence - including the shooting deaths of two bailiffs at a courthouse in MI today - President Barack Obama has the hard task of trying to heal Americans' growing rifts over race and policing.
Police revealed additional details today, saying 11 officers fired back at Johnson and two others controlled the robot.