In recent weeks China - primarily through its Ambassador to Australia Jingye Cheng - has "bristled" at Australia's call for an independent global investigation into the origins of the virus.
The Ambassador first threatened a potential consumer boycott on Australian exports, and then on Tuesday leaked a private conversation with Secretary of the Department of Foreign Affairs and Trade Frances Adamson.
"You'd think China would welcome it but instead they take it as a slight, and worse they bully Australia through their ambassador," he said.
Mr Kenny said the issue of an international investigation should be about "shared global vulnerability and therefore global co-operation".
"It's time we heard from many more countries on this, supporting Australia's logical position, and putting pressure on Beijing".
Resources Minister Keith Pitt told Mr Kenny what is important is "ensuring what's happening right around the world right now never ever again".