The Former Japanese Prime Minister died aged 67 after he was shot twice on Monday morning in the eastern city of Nara during an election campaign event.
The latest gaffe took place during Biden's speech where he announced new steps aimed at protecting women's reproductive rights following the Supreme Court's decision.
Under Hong Kong law, anyone found exposing themselves in public could face a fine of 1,000 Hong Kong dollars (approximately $127) and a six-month jail sentence.
Following the shooting, which took place on Monday, the eight officers who were directly involved in the shootout have been placed on administrative leave.
Giuliani was campaigning for his son Andrew, who is running as a Republican candidate for governor of New York, when the incident took place on Sunday.