China and Iran are calling for the release of Nicolás Maduro and his wife Cilia Flores.
China’s foreign ministry says the US’ actions are “a clear violation of international law and basic norms governing international relations”.
It has reportedly called on Washington to “cease efforts to subvert the Venezuelan government and resolve issues through dialogue and negotiation”.
Iran, a close ally of Venezuela, says the pair was abducted.
According to AFP foreign ministry spokesman Esmail Baqaei said “It’s nothing to be proud of; it’s an illegal act.”
Mr Maduro is expected to appear in a New York court after being captured during US air strikes on the country on Saturday.
He is accused by the US of drug trafficking and weapons offences, and of running a “narco-terrorist” regime – a claim he denies.