The 54-year-old, who lives in Maryland, has written an open letter as the state's general assemblydebates a bill which would prevent the use of live elephants for entertainment in the US state.
Carwyn Jones said that while he very rarely complained about what was said during robust debates in the Assembly, he felt Mr Davies' comments had "crossed a boundary".
You're very fond of bemoaning in your comments that real life rarely intrudes too closely on debates in the Assembly over sub clauses in legislation and arguments over policy points.