He hopped a five-foot fence near the US Treasury Department, which is located next to the White House, then climbed an eight-foot vehicle gate and a shorter fence near the southeast corner of the East Wing of the White House grounds before he was caught, the Secret Service said.
"The Secret Service can confirm that at no time did the individual gain entry into the White House," the statement said.
Tran, from Milpitas, California, set off several alarms after jumping the fence but was able to avoid other sensors before he was discovered just steps from the main building, CNN reported on Friday.
The network also reported that Tran was spotted "looming around" Washington's Pennsylvania Avenue, where the White House is located, nearly six hours before his arrest.
The incident prompted Jason Chaffetz, chairman of the House of Representatives oversight committee, to request that Secret Service Acting Director William Callahan provide a briefing on Monday. In a letter to Mr Callahan on Friday, Mr Chaffetz referred to allegations that Tran moved undetected around the grounds "for a considerable amount of time."
"The Committee has longstanding concerns regarding repeated security incidents at USSS-protected facilities," Mr Chaffetz wrote. He noted that a 2015 committee report on the Secret Service found 143 breaches and attempted breaches over a 10-year period.
"The moment somebody jumps over the fence they have to be taken down," Mr Chaffetz later told CNN. "This one scares me probably more than any because of the length of time, the proximity to the president, getting right up close to the White House and going so long without being detected. It makes no sense. I don't know what in the world they're doing but it is a total and complete embarrassment."
The Secret Service said it was taking additional steps to prevent security lapses.
Tran told federal agents that he was a friend of the president and had an appointment, according to court documents. He was carrying two cans of mace, a US passport, a computer and one of Mr Trump's books, authorities said.
Mr Trump commended the Secret Service for doing a "fantastic job" apprehending Tran.
Tran was released with no bail on Monday and returned to California, where he must submit to GPS monitoring until his next hearing in Washington.
The intrusion was the latest in a series of breaches at the White House in recent years. Security has been boosted, including the installation in 2015 of sharp spikes on top of the black iron fence that circles the 18-acre property.
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