The visa restrictions would 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.
The secretary of state also warned that "these visa restrictions may also be used to deter ICC efforts to pursed allied personnel including Israelis without allies' consent".
Claiming that the implementation of the policy had already begun, Pompeo did not reveal the identities of people at the Hague-based court who have or will be affected. "We are prepared to take additional steps, including economic sanctions, if the ICC does not change course".
Pompeo's remarks come as the US National Security Advisor John Bolton in a speech on last September threatened the ICC and its staff with sanctions if it proceeds investigations into alleged war crimes by American troops in Afghanistan.
Human Rights Watch called the announcement a "thuggish attempt to penalize investigators" at the court.
Friday's actions by the State Department followed a September 2018 threat from National Security Adviser John Bolton that the U.S. would "use any means necessary to protect our citizens and those of our allies from unjust prosecution by this illegitimate court".
"The ICC is attacking America's rule of law", Pompeo told reporters. "It reeks of the very totalitarian practices that are characteristic of the worst human rights abusers, and is a blatant effort to intimidate and retaliate against judges, prosecutors, and advocates seeking justice for victims of serious human rights abuses".
Last year, President Donald Trump told the United Nations General Assembly that the USA would never surrender its sovereignty by supporting the ICC and would always regard it as an illegitimate global institution.
"If you're responsible for the proposed ICC investigation of U.S. personnel in connection with the situation in Afghanistan you should not assume that you still have, or will get, a visa or that you will be permitted to enter the United States", Pompeo added.
Al Jazeera's Patty Culhane, reporting from Washington, said ICC investigators were also seeking to probe the U.S. military's conduct "not just in Afghanistan, but also in black sites that we now know was spread across the globe, where they were held in secret detention for months, and where some say detainees were tortured". While she didn't target the US military, Bensouda said the inquiry sought "support and cooperation" from the Afghan government, other state parties and the worldwide community as a whole "to accomplish our objectives of ensuring accountability for the crimes committed and that the long-suffering victims of those crimes receive justice".
"This announcement is the latest attack on global justice and worldwide institutions by an administration hellbent on rolling back human rights protections".
The International Criminal Court is supported by 123 nations, including Switzerland.
It said that all states were obliged to prosecute and punish the most serious crimes.