"As WikiLeaks stands under threat, so does the freedom of expression and the health of all our societies. We must use this moment to articulate the choice that is before the government of the United States of America," he said.
"Will it return to and reaffirm the revolutionary values it was founded on or will it lurch off the precipice, dragging us all into a dangerous and oppressive world in which journalists fall silent under the fear of prosecution and citizens must whisper in the dark?
"I say it must turn back. I ask President Obama to do the right thing: the United States must renounce its witch-hunt against WikiLeaks."
There must be no "foolish talk" of prosecuting media organisations, be it WikiLeaks or be it the New York Times newspaper.
Assange also called on the US to end its "war on whistleblowers", and demanded that Bradley Manning, the US army intelligence analyst suspected of leaking the information, be released.
He has been charged with transferring classified data and delivering national defence information to an unauthorised source and faces up to 52 years in jail.
Assange described Manning as a hero and "an example to all of us", which drew cheers from scores of supporters.
"On Wednesday, Bradley Manning spent his 815th day of detention without trial," said Assange. "The legal maximum is 120 days."
Assange referred to recent jailings of people for exercising their freedom of speech and called for enthusiastic opposition to such oppressive actions.
"There is unity in the oppression. There must be absolute unity and determination in the response."
"I am here today because I cannot be there with you today. But thank you for coming, thankyou for your resolve, your generosity of spirit.
"On Wednesday night, after a threat was sent to this embassy, the police descended on this building. You came out in the middle of the night to watch over it, and you brought the world's eyes with you.
"Inside this embassy in the dark, I could hear teams of police swarming up inside the building through its internal fire escape.
"But I knew there would be witnesses, and that is because of you.
"If the UK did not throw away the Vienna Conventions the other night, it is because the world was watching. And the world was watching because you were watching.
"So the next time that somebody tells you that it is pointless to defend those rights that we hold dear, remind them of your vigil in the dark before the embassy of Ecuador. Remind them how, in the morning, the sun came up on a different world, and a courageous Latin American nation took a stand for justice."