It happened on Bronxwood Avenue in the Williamsbridge section of the Bronx.
Police sources said the suspect and the victim were arguing inside the deli just after 1:30 p.m. when the victim was shot.
The person the victim was arguing with inside the deli was not an employee, police said.
The 20-year-old was taken to Jacobi Hospital, where he later died, police said.
Police are looking into whether the motive of the dispute could be gang-related based on previous interactions with law enforcement.
The suspect is a male and fled on foot.
Police said the suspect was wearing a black shirt with flowers on it and a vest.
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