Artificial intelligence (AI) firm Anthropic has filed a first of its kind lawsuit against the US government over claims that it is a "supply chain risk".

The AI firm's chief executive Dario Amodei and Defence Secretary Pete Hegseth have been publicly rowing due to the company's refusal to allow the military unfettered use of its AI tools.

The Pentagon retaliated by making Anthropic the first US company to be labelled a "supply chain risk", but Anthropic said in its lawsuit on Monday against a list of US government agencies that this was unlawful and unprecedented.

A spokesman for US Department of Defense declined to comment citing a policy on active litigation.

"These actions are unprecedented and unlawful," Anthropic said of its risk designation.