The European Union - another critic - "better choose purgatory, hell is filled up", Mr Duterte said.
The remarks came as the US and the Philippines began joint military exercises. The US said there was a "strong alliance" with the Philippines.
Mr Duterte's drugs war has caused thousands of extrajudicial killings.
In a speech to local officials and business executives Mr Duterte said he was disappointed with the US for criticising the Philippines' tactics to combat the drug trade. He also described Washington as an unreliable ally.
