A law enforcement official with knowledge of the investigation into what happened said the man had been making threats against law enforcement.
The official wasn't authorized to release details of the investigation and spoke on the condition of anonymity.
Boston Police Commissioner William Evans said members of the Joint Terrorism Task Force approached Usaama Rahim in the city's Roslindale neighborhood yesterday morning to question him about "terrorist-related information" they had received when he went at officers with a large military-style knife.
Rahim, 26, was taken to a hospital, where he was pronounced dead.
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Evans would not disclose why Rahim was under surveillance. But Evans said a "level of alarm" prompted authorities to try to question him.
"Obviously, there was enough information there where we thought it was appropriate to question him about his doings," Evans said. "He was someone we were watching for quite a time."
Evans said the officers didn't have their guns drawn when they approached Rahim. He said police have video showing Rahim "coming at officers" while they are backing away.
That account differs from one given by Rahim's brother Ibrahim Rahim, who said in a Facebook posting that his youngest brother was killed while waiting at a bus stop to go to his job.
"He was confronted by three Boston Police officers and subsequently shot in the back three times," he wrote. "He was on his cell phone with my dear father during the confrontation needing a witness."
The Suffolk district attorney's office and the FBI said they will investigate Rahim's shooting, a routine procedure for shootings involving police.
The Council of American-Islamic Relations will monitor the investigation, spokesman Ibrahim Hooper said.