The International Criminal Court said on Tuesday it would "continue to do its work undeterred".
This came a day after US National Security Adviser John Bolton threatened sanctions if the court investigated US activities in Afghanistan.
The Hague-based court said in a statement it was an independent and impartial institution with the backing of 123 countries.
"The ICC, as a court of law, will continue to do its work undeterred, in accordance with those principles and the overarching idea of the rule of law," it said.
ICC prosecutor Fatou Bensouda said last year there was a "reasonable basis to believe" war crimes and crimes against humanity were committed in Afghanistan.
She further held that all sides in the conflict would be examined, including members of the US armed forces and Central Intelligence Agency.
But Bolton said on Monday that if such an investigation was launched, the Trump administration would consider banning ICC judges and prosecutors from entering the United States.
He further threatened sanctioning funds the judges have there and prosecuting them in US courts.
The United States did not ratify the Rome treaty that established the ICC during the presidency of Republican George W. Bush.
Instead, it adopted the American Services-Members’ Protection Act, nicknamed the Hague Invasion Act because it authorised the use of any means necessary to free US personnel held by the court.