"My fellow Americans... " Obama, who was born is the US state of Hawaii from a US mother, said at a dinner of White House correspondents.
"Call Disney if you don't believe me," he said, in a reference to conservative conspiracy theories that Obama is not a "natural born" US citizen, a constitutional requirement for presidential eligibility.
Obama directed his humor at real estate mogul Donald Trump, a 2012 Republican presidential hopeful who expressed serious doubts about Obama's citizenship.
"Now I know that he has taken some flak lately, but no one is happier, no one is prouder to put this matter to rest than Donald," Obama said of Trump.
The president jokingly advised Trump to "get back to focusing on the issues that matter like 'Did we fake the Moon landing?' 'What really happened at Roswell?" and 'Where are Biggie and Tupac?'"
The Roswell incident occurred in 1947 when an strange flying object that crashed in the general vicinity of Roswell, New Mexico. The military, which quickly cordoned off the site of the crash, said it was an experimental weather balloon, while others insist to this day it was an extra-terrestrial spacecraft with alien occupants.