The US president says the Syrian Opposition Council is now "inclusive enough" to be granted greater legitimacy in the international community.
"Obviously, with that recognition comes responsibilities," Obama said in an interview on Tuesday with ABC News.
"To make sure that they organise themselves effectively, that they are representative of all the parties, that they commit themselves to a political transition that respects women's rights and minority rights."
The move paves the way for greater US support as the group seeks the ouster of Syrian President Bashar Assad.
Recognition of the council as the sole representative of Syria's diverse population brings the US in line with Britain, France and several of America's Arab allies, which took the same step shortly after the body was created at a meeting of opposition representatives in Qatar last month.
Obama's announcement follows his administration's blacklisting of a militant Syrian rebel group with links to al-Qaeda.
That step is aimed at blunting the influence of extremists amid fears that the regime may use or lose control of its stockpile of chemical weapons.