Chief Jeff Davis said a video taken by a bystander showed the incident but that the department declined to release it at this time. He also declined to identify the object.
Davis said the man refused multiple instructions from an officer and "concealed his hands in his pockets." He said the man "drew an object from his front pants pockets, placed both hands together on it and extended toward the officers."
One officer fired a Taser and another fired rounds from his handgun. No weapon was recovered at the scene.
"Now is the time for calm," Davis said "Now is the time for the community to work with us."
The shooting sparked protests in the San Diego County city, with friends of the man's family saying he suffers from a mental illness and did not pose a threat to the officers.
The man, who was believed to be age 30, was taken to a hospital with unspecified injuries.
A crowd of about 30 people gathered at the shooting scene. By the evening, the crowd grew to about 100 people, including community leaders and members of local churches.
Most of the demonstrators voiced concerns that the shooting was racially motivated.
The El Cajon violence comes amid growing national debate over police shootings of African Americans. Charlotte was rocked by days of protests last week after police fatally shot 43-year-old Keith Lamont Scott.
Police received three calls about a man acting "erratically" near a strip mall on Broadway near Mollison Avenue shortly after 2 p.m., El Cajon police Lt. Rob Ransweiler said. One caller told them the man was walking in traffic, he said.
Officers said the man refused to follow their orders, spurring a confrontation that led to at least one officer opening fire outside the apartment building adjacent to the strip mall.
Officers provided first aid until paramedics arrived and took the man to a hospital.
On Twitter, the department disputed some of the claims made by protesters: "The investigation just started, but based on the video voluntarily provided by a witness, the subject did NOT have his hands up in the air."
Michael Ray Rodriguez said he was driving away from the apartment building when he saw a shirtless black man with his hands in the air. In a matter of seconds, he said, an officer opened fire.
The officer "shot him again and again," Rodriguez said, adding he heard five shots.
El Cajon police officers are not equipped with body-worn cameras. The department recently completed a pilot program to test the cameras and ordered some. The equipment has not been delivered, Ransweiler said.
He said a witness voluntarily turned over a cellphone that contains video of the shooting.
The district attorney's office and the El Cajon Police Department are investigating.
Davis said a witness voluntarily turned over a cellphone that contains video of the shooting but the department does not plan to release the footage. A new county-wide protocol embargoes footage of officer-involved shootings until the District Attorney's Office investigates them.
El Cajon police officers are not equipped with body-worn cameras. The department recently completed a pilot program and ordered some cameras but officers have not yet been equipped.
The victim was identified by family friends as Alfred Orlango, 30.
David Hernandez writes for the San Diego Union-Tribune.
Follow @lanow for breaking news.
7:15 a.m.: Updated with quotes from chief and other details.
10:25 p.m. This story was updated to reflect that the man has died.
9:12 p.m. This story was updated throughout with more details.
8:12 p.m. This story was updated with additional information from the scene, as well as family members saying the man who was shot suffers from mental illness.