Broome's weapon was recovered, Lovett said, adding the officer never lost control of it.
The suspect was armed only with a knife and "never took the officer's gun," Lovett said.
Police have a "person of interest that we're seeking," Lovett said, and he is from the west Savannah area.
"From the information we have, we don't think he would've gone too far from where he lives," he said.
"It is going to be a long haul" before he is apprehended, the chief added, "but we're prepared for that."
The suspect is described as a black man in his 20s, 5-foot-11 to 6-feet tall, weighing about 175 pounds. He has a short haircut and was wearing a red shirt, long black shorts and black shoes.
Broome, an 11-year veteran, was shot twice, once in the chest by a bullet that struck his metal nameplate, and a second round that struck his side but was stopped by his bullet-proof vest, Lovett said.
That slug was not recovered.
"It probably fell out on the ground somewhere during the struggle," Lovett said.
The assailant initially cut Broome on his left forearm after he came at the officer "at a very high rate of speed," Lovett said.
Broome was released from Memorial University Medical Center on Thursday. Pieces of the metal nameplate were removed from his chest wound.
"It was not superficial," Lovett said during a discussion with local media. "It was actually a quarter-inch hole in his chest."
A number of people were questioned after the attack, the chief said, but no one was arrested.
Beyond the statement by Lovett, the department is releasing little information. "Our investigators are working very hard," said Metro spokeswoman Gena Moore, but no additional details were released.
The incident started after Broome approached a man who looked suspicious about 12:45 p.m. Thursday in a dirt lane near Lathrop Avenue, police said. The struggle ensued, and Broome was able to call a "Signal 13" distress call to bring other officers rushing to the scene.
Lovett said he did not know the officer personally, explaining Broome had been on special assignment for some time and only came back to the department in November.
"I haven't had any bad reports (about Broome), so that's a good thing," Lovett said.
He said the local department is receiving assistance from a number of other agencies.
For the chief, the attack was personal.
"This is my family,'' he said. "When you attack a police officer, you're attacking the whole family.''