"We are determined to protect the American and allied military and civilian personnel from living in fear of unjust prosecution for actions taken to defend our great nation".
Pompeo said the new visa restrictions would include "persons who take or have taken action to request or further such an investigation".
Pompeo's announcement came after John Bolton, President Donald Trump's national security adviser and a longtime critic of the ICC, threatened to impose sanctions on court officials in September if they continued to pursue an investigation of potential crimes by us civilians or military personnel in Afghanistan.
The United States announced its first sanctions against the International Criminal Court Friday, threatening visa restrictions for anyone involved in a potential probe of American soldiers' actions in Afghanistan.
"Attacking worldwide judicial actors for doing their jobs undermines global efforts to hold to account those most responsible for atrocity crimes such as torture and mass murder", Goldston said.
"But that's not how law works, " he said on Twitter.
The Trump administration in September said that if the court launched a probe of war crimes in Afghanistan, it would consider banning ICC judges and prosecutors from entering the United States, sanctioning funds they have there and prosecuting them in USA courts.
In November 2017, ICC prosecutor Fatou Bensouda sought authorization to open an investigation into crimes connected to the conflict in Afghanistan.
Judges are reviewing all material submitted by the prosecutor, and must decide whether or not to authorise an investigation. The Palestinians have asked the ICC to investigate Israel for alleged human rights abuses.
The ICC has not yet made a decision on whether to authorize that investigation.
Supporters of the court slammed Pompeo's announcement on Friday.
Human Rights Watch called it "a thuggish attempt to penalize investigators" at the International Criminal Court.
This past September, Bolton said the ICC was a direct threat to U.S. national security interests and he threatened its personnel with both visa revocations and financial sanctions should it try to move against Americans. "Taking action against those who work for the ICC sends a clear message to torturers and murderers alike: Their crimes may continue unchecked".
Daniel Balson, advocacy director at Amnesty International USA, noted that this is just "the latest attack on international justice and international institutions by an administration hellbent on rolling back human rights protections". Only if they were unable or unwilling to do so may the ICC intervene.
James Goldston, executive director of the Open Society Justice Initiative, said Pompeo's remarks reflected the administration's view that global law matters "only when it is aligned with USA national interests".
He said the United States declined in 1998 to join the court "because of its broad, unaccountable prosecutorial powers and the threat it poses to American national sovereignty".