"I ask President Obama to do the right thing, the United States must renounce its witchhunt against WikiLeaks," said Assange, making his first public statement since being granted political asylum by Ecuador on Thursday.
Assange praised the "courage" shown by the Latin American nation's President Rafael Correa in giving him asylum, a move which has angered Britain which has said it will continue to seek his extradition to Sweden.
"I thank President Correa for the courage he has shown in considering and in granting me political asylum," Assange told journalists and several dozen of his supporters gathered outside the embassy in an upmarket part of London.
The 41-year-old Australian walked into the embassy two months ago after exhausting all legal avenues in Britain in his bid to avoid being sent to Sweden, where he is wanted for questioning over sex crimes.
Assange claims the accusations against him -- made by two female WikiLeaks volunteers -- are politically motivated and insists that he will eventually be extradited to the United States.
WikiLeaks enraged Washington by releasing video of a US attack in Iraq, as well as tens of thousands of classified US documents about the wars in Iraq and Afghanistan.
Assange made the speech from the balcony to avoid leaving the embassy premises and being arrested by the police officers surrounding the building.
Britain has said it could invoke a little-used piece of legislation introduced in 1987 which it says allows it to revoke the diplomatic immunity of an embassy on British soil and go in to arrest Assange.
The warning was seen as a threat by Ecuador which condemned it.
However, Britain now says it would prefer a negotiated solution.
Thanking his supporters, Assange claimed that he had heard police trying to enter the building after he was given asylum.
"Inside this embassy after dark, I could hear teams of police swarming up into the building through its internal fire escape," he told them. "But I knew there would be witnesses, and that is because of you."
With a new spiky haircut and wearing a blue shirt and maroon tie, Assange claimed Britain had "thrown away" the Vienna Conventions in warning Ecuador that it could enter the building to extract him.
Despite Ecuador providing a haven for Assange, British Foreign Secretary William Hague has said Britain had no choice but to seek his extradition.
Ahead of Assange's appearance Sunday, his high-profile Spanish lawyer Baltasar Garzon said the former hacker was in "fighting spirit".
Reading from a statement outside the embassy, Garzon said: "I have spoken to Julian Assange and I can tell you that he is in fighting spirit."
Garzon said Assange had instructed his lawyers "to carry out a legal action in order to protect the right of WikiLeaks, Julian himself and all those currently being investigated."
WikiLeaks on Sunday urged Sweden to guarantee it would not extradite him to the United States.
"It would be a good basis to negotiate a way to end this matter if the Swedish authorities would declare without any reservation that Julian would never be extradited from Sweden to the USA," WikiLeaks spokesman Kristinn Hrafnsson told AFP.
Assange is said to be living in a small room within the embassy, which is situated in Knightsbridge near to the Harrods department store.
His mother on Sunday expressed confidence that her son would eventually make it to Ecuador to continue his whistleblowing work.
"He's had billions of people around the world supporting him, the US and their allies are almost alone on this one and the support grows day by day," she told Australia's ABC 24.
"It could be that the UK government decides to backtrack from this position of being the US lap dog and stands up for its own sovereignty as well as the sovereignty of Ecuador."
The Latin American country has meanwhile received powerful backing from regional allies as they warned Britain of "grave consequences" if it breaches diplomatic security at the London embassy.
Foreign ministers from the Venezuela-led so-called Bolivarian Alliance for the People of Our America (ALBA) flew to Ecuador on Saturday to demonstrate full diplomatic support.