BOSTON -- Blurry surveillance video raises new questions about the fatal shooting of a Boston man by terrorism investigators, his family said.

Usaamah Rahim's family insists the video, released by authorities Monday, doesn't show the 26-year-old security guard brandishing a weapon or approaching officers aggressively.

They say many unanswered questions remain about the June 2 incident, including if deadly force was necessary and whether it was appropriate to approach Rahim in a "military-like formation" without a warrant.

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"The family asks that the public keep an open mind," it said in a statement. "The video reveals part of the story, but not the entire story."

Authorities said the video confirms officers acted responsibly, drawing their guns only after backing away and giving Rahim multiple chances to drop the military-style knife he was holding.

"We averted a serious tragedy that day," Police Commissioner William Evans said at a news conference where the video was released. "I don't think he was going to go down very easy. ...We can second-guess this, but it unraveled so quickly. I believe my officers acted responsibly."

The FBI and Boston police said they had Rahim, who is black and Muslim, under 24-hour surveillance and had intercepted conversations suggesting he planned to carry out an attack on police.

The brief video, which has no audio, shows a man identified by police as Rahim walking through a parking lot on his way to a bus stop in the city's Roslindale neighborhood.

Six officers, who authorities say were in plainclothes, approach Rahim but appear to back up as Rahim advances toward them.

The officers encircle Rahim and then draw their firearms. Rahim, who is mostly obscured by a light pole during the altercation, falls to the ground a few moments later.

Police said two officers - an FBI agent and a police officer - fired three shots.

Authorities last week showed the video to black and Muslim community leaders and Rahim's family.

Authorities say Rahim planned to carry out an Islamic State of Iraq and Syria (ISIS)-style beheading, possibly of controversial conservative activist and outspoken Islam critic Pamela Geller, CBS News correspondent Jeff Pegues reported.

"I'm the number one target for ISIS right now," Geller told CBS News.

On May 3, Geller organized the Prophet Muhammad cartoon drawing contest in Garland, Texas, where police fatally shot two men who opened fire outside the event. Geller told CBS News she has increased her security but has yet to discuss the threat with the FBI.

"It won't end with me or the cops," she said. " ... The one thing that's came out of Garland is ISIS is here. Islamic terrorism is here on the home soil on a weekly, sometimes a daily basis."

Law enforcement sources are still unclear how serious the plot against Geller was and how much of it was just talk.