Story highlights The suspect's family says they are "shocked, horrified and heartbroken"

Jackson said he wanted to kill more black men in Times Square, officials say

(CNN) The white man accused of fatally stabbing a black man in New York on Monday night told police he targeted the victim because he was black and that he viewed the killing as "practice," according to a criminal complaint.

The suspect, 28-year-old James Harris Jackson, told police he intended to go to Times Square to kill more black men, according to the complaint.

Jackson was arraigned on second-degree murder and weapons charges in Manhattan Criminal Court on Thursday, a day after he turned himself in to police.

Prosecutor Joan Illuzzi-Orbon said in court that the charge may be upped to first-degree murder because it was likely an act of terrorism , according to a spokesperson for the district attorney's office.

Police said Jackson singled out Timothy Caughman, 66, and stabbed him with a sword multiple times while Caughman was sifting through garbage late Monday night. A bleeding Caughman stumbled to a nearby police substation and was then taken to a hospital, where he was pronounced dead.

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