The Trump administration also said restrictions may also be placed on investigators examining alleged war crimes involving Israel.
Suggesting they would not be granted visas, Pompeo said: “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.”
A spokesperson for the ICC said that it was an independent and impartial institution and would continue its work “undeterred” by Washington’s actions.
A prosecutor currently has a pending request to investigate actions of US troops in Afghanistan.
The visa restrictions will apply to any ICC employee who takes or has taken action “to request or further such an investigation” into allegations against US forces and their allies in Afghanistan that include forced disappearances and torture, Mr Pompeo said.
The new policy is designed to deter the investigators, he added.
“These visa restrictions may also be used to deter ICC efforts to pursue allied personnel, including Israelis, without allies’ consent,” he said. “If you are responsible for the proposed ICC investigation of US personnel in connection with the situation in Afghanistan, you should not assume that you still have or will get a visa or will be permitted to enter the United States.”
“We are prepared to take additional steps, including economic sanctions, if the ICC does not change its course,” Mr Pompeo said, adding: “The first and highest obligation of our government is to protect its citizens and this administration will carry out that duty. The ICC, as a court of law, will continue to do its independent work, undeterred, in accordance with its mandate and the overarching principle of the rule of law.”
Mr Pompeo’s announcement was criticised by Human Rights Watch, which called it “a thuggish attempt to penalize investigators” at the ICC.
“The Trump administration is trying an end run around accountability,” the organisation said. “Taking action against those who work for the ICC sends a clear message to torturers and murderers alike: Their crimes may continue unchecked.”