At the meeting of the Union of South American Nations (UNASUR) on Sunday, the 12 foreign ministers from the continent's countries said they hoped that the dispute could be resolved through negotiation.
"We reiterate the right of states to grant political and diplomatic asylum," the bloc's joint statement read.
Ministers at the UNASUR meeting, pictured above, were also critical of Britain's role in the diplomatic conflict, expressing "solidarity with and support for the government of Ecuador in the face of threats against its embassy in Britain."
Assange has been holed up at the Ecuadorian embassy in London since June 19, when he walked into the embassy after exhausting all legal avenues in Britain to fight his extradition to Sweden, where he is wanted over alleged sex crimes. He denies the charges.
WikiLeaks infuriated the United States and its allies by using its website to expose hundreds of thousands of classified US diplomatic and military communiqués in 2010. Documents included video of a US attack in Iraq.
Ecuador granted Assange asylum at the embassy despite warnings from the British government that it could envoke the Diplomatic and Consular Premises Act of 1987, which would allow it to revoke the embassy's dimplomatic immunity on British soil.
Assange appeared on the balcony of Ecuador's embassy in London earlier on Sunday, praising the "courage" shown by the nation's president, Rafael Correa in granting him asylum.
"I thank President Correa for the courage he has shown in considering and in granting me political asylum," Assange told the contingency of international media gathered outside the embassy.
Assange rebuked the US for threatening freedom of expression and called on US President Barack Obama to stop its "witch hunt" against his whistle-blowing website, as supporters cheered.
"I ask President Obama to do the right thing, the United States must renounce its witch hunt against WikiLeaks."
The accusations, Assange said, are politically motivated. He believes the US wishes to put him on trial for divulging state secrets.
Assange added the US risked thrusting the world into an era of journalistic oppression: "As WikiLeaks stands under threat, so does the freedom of expression and the health of all our societies."
In his ten minute speech from the embassy's balcony, where he is staying to avoid arrest by British police, Assange demanded that Bradley Manning, a US army intelligence analyst and suspected source of leaking confidential US diplomatic communiqués to WikiLeaks, be released from a US prison.
On Friday, an emergency meeting of the foreign ministers of the Organisation of American States (OAS) will take place in Washington D.C. to talk about the issue of his asylum, Assange said.
The OAS Permanent Council called for the meeting Friday at Ecuador‘s request in a vote of 23 in favour and only three - the United States, Canada and Trinidad and Tobago - against. Five other countries abstained.
OAS Secretary General José Miguel Insulza said: "The central issue is not the right of asylum, it is the inviolability of embassies."
Insulza recalled that last year the United Nations Security Council ruled "very strictly on the absolute immunity that diplomatic missions must have in all the countries of the world."
mz/jlw /ipj (dpa, Reuters, AFP, AP)