Micah Johnson, a black Army veteran, insisted on speaking with a black negotiator and wrote in blood on the wall of a parking garage where police cornered and later killed him, David Brown told CNN’s State Of The Union.
Investigators are now trying to decipher the writing by looking through evidence from his suburban Dallas home, Brown said.
The chief defended the decision to kill Johnson with a bomb delivered by remote-controlled robot, saying negotiations went nowhere and officers could not approach him without putting themselves in danger.
Mr 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”.
Johnson had practised military-style drills in his garden and trained at a private self-defence school that teaches special tactics, including “shooting on the move”.
On Friday, Dallas Mayor Mike Rawlings described Johnson as “a mobile shooter” who had written manifestos on how to “shoot and move”.
Authorities have said the gunman kept a journal of combat tactics and had amassed a personal arsenal at his home, including bomb-making materials, rifles and ammunition.
Johnson donned a protective vest and used a military-style semi-automatic rifle for the shootings, which marked the deadliest day for US law enforcement since 9/11.
In all, 12 officers were shot, five fatally, just a few blocks from where President John F Kennedy was assassinated in 1963.
Johnson was a private first class with a speciality in carpentry and masonry. He served in the Army Reserve for six years starting in 2009 and did one tour in Afghanistan from November 2013 to July 2014, the military said.
The attack began on Thursday while hundreds of people were gathered to protest against the police killings of Philando Castile, who was shot in Minnesota, and Alton Sterling, who was shot in Louisiana after being pinned to the pavement by two white officers.
Video showed protesters marching along a street near City Hall when shots erupted.