Dominic Adesanya, 23, was stopped on a lawn near the building. He was unarmed.
Video footage of the incident showed Dominic Adesanya kicking and punching Secret Service dogs who had been set on him.
The latest incident comes a month after a man armed with a knife scaled the fence and made it inside the White House.
That, and other questions about security at the White House, lead to the resignation of the head of the Secret Service, Julia Pierson.
A spokesman for the agency said charges were pending against Dominic Adesanya.
Two dogs have been taken to the vet for treatment for their injuries, the spokesman added.
Meanwhile, it has emerged that in 2011, the Secret Service diverted agents from their duties at the White House to the home of an agency employee caught in a personal dispute with a neighbor.
The inspector general of the Homeland Security Department, John Roth, called the conduct a “serious lapse of judgement”.
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