It happened just before 11:30 p.m. Thursday at St. John's Place and Troy Avenue.
Adiyb Ramkissoon, 30, was found inside the deli with gunshot wounds to his torso.
Crime scene investigators are working to determine who was chasing him and why. Police say he lived nearby.
They have been reviewing security camera footage and interviewing witnesses.
The suspect was last seen wearing a green jacket, black pants, blue hat and white sneakers. He was last seen fleeing on foot eastbound on St. John's Place.
The NYPD is asking for the public's help tracking down the suspect.
Call the NYPD's Crime Stoppers Hotline at 1-800-577-TIPS (8477) or for Spanish, 1-888-57-PISTA (74782). You can also submit tips by visiting the CrimeStoppers website at crimestoppers.nypdonline.org or by messaging on Twitter @NYPDTips.
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