Thanking his supporters and especially Ecuador, which has granted him diplomatic asylum despite threats from the UK, Assange asked US President Barack Obama to "to stop witch-hunt against WikiLeaks".
"I ask President Obama to do the right thing, the United States must renounce its witch-hunt against WikiLeaks," he said.
The 41-year-old also asked the US to release Bradley Manning, charged with leaking classified information.
Assange thanked Ecuadorean President Rafael Correa for the "courage he has shown," in granting him asylum.
Assange's appearance on the balcony is seen as an attempt to avoid arrest. The Australian national is wanted by Sweden for questioning over alleged sexual misconduct.