The suspects were identified as Evan J. Graham and Vaughn Greenbrier Lerriche, according to NBC television.
Graham threw over the north fence of the presidential mansion an object that looked like a cassette tape and Lerriche threw various papers over the south fence.
Authorities are investigating whether the two incidents are related.
President Barack Obama left Washington Wednesday on a tour that Thursday took him to California to participate in a Democratic Party fundraising event.
The incidents came two days after an inattentive driver followed the motorcade carrying the president's daughters back to the White House and entered the zone barred to traffic in front of the mansion, where he was stopped by presidential security personnel, arrested and charged with unlawful entry.