Twenty-three countries voted on Friday for the resolution proposed by Ecuador to convene the meeting at its Washington headquarters to discuss Quito's stand-off with Britain over Assange. The US, Canada and Trinidad and Tobago voted no.
The vote was taken at emergency talks to discuss the Assange case.
Assange, a 41-year-old Australian national, took refuge at Ecuador's embassy in London on June 19 to avoid extradition to Sweden, where he is wanted for questioning over alleged sexual misconduct.
Ecuador granted diplomatic asylum to Assange on Thursday, triggering a diplomatic row with the British government, which angrily insisted it would still move to extradite him.