The shooting took place around 4am (0800 GMT) inside a Pathmark store in the town of Old Bridge in the state of New Jersey, broadcaster WABC reported on its website.
Store employees were apparently stocking shelves when the gunman entered. Authorities believe he killed two people before committing suicide, according to WABC.
It was not clear how many people were shot before before police arrived on the scene.
Authorities could not immediately be reached for confirmation.
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