Police say the man was found around 8 a.m. Thursday rummaging through a desk in a secretary's office in the basement of George Washington Elementary School in Union City.
The school was placed under lockdown as a precaution.
The Jersey Journal reports Police Chief Richard Molinari said the man fled into a stairwell and exited the building. He remains at large.
Later Thursday, the Daniel Webster Elementary School in Weehawken was locked down at about 4 p.m. after an apparent burglary attempt that police believe may be connected. Classes were over by that time, but 57 students who were participating in after-school programs had to be escorted out of the building while they investigated.
The lockdown was lifted at about 6 p.m.
The unidentified man was captured on surveillance video at both schools, but managed to escape undetected. It's not clear what his motive was.
Police said the Weehawken school will be open Friday, with a visible police presence outside and undercover officers inside.
Authorities released a surveillance image of the suspect (above) wearing a hat and carrying a backpack.
-- Ida Siegal contributed to this report.