Assange spoke from a balcony window at Ecuador's embassy in central London, meaning he did not leave its official premises.
The WikiLeaks founder addressed a crowd of media and cheering supporters who had gathered on the street below, asking US President Barack Obama to "do the right thing."
"The United States much renounce its witchhunt against WikiLeaks," Assange said, in a prepared statement broadcast by TV news networks around the world.
Assange also demanded the release of Bradley Manning, WikiLeaks' suspected source of US diplomatic cables, who is being held in a US prison.
Ecuador last week granted Julian Assange political asylum, two months after he took refuge in its London embassy.
Assange holed up in the embassy to avoid extradition to Sweden for questioning over alleged sexual offenses. He also fears extradition to the United States in connection with the leaked diplomatic cables published by his WikiLeaks website.
The 41-year-old faces arrest by police if he sets foot on British soil.
According to the BBC's live broadcast, in his statement today, Assange said:
"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 asked: "Will it return to and re-affirm 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."
Assange also referenced Pussy Riot, the Russian protest punk band that saw three of its young women members found guilty of hooliganism for an anti-Vladimir Putin protest at Moscow's Cathedral of Christ the Savior.