Pompeo, acting on a threat delivered in September by USA national security adviser John Bolton, framed the action as necessary to prevent the worldwide body from infringing on US sovereignty by prosecuting American forces or allies for torture or other war crimes.
Pompeo wants to circumscribe the unbiased ICC and have any wrongdoing committed by American personnel dealt with in USA military and criminal courts.
"The ICC is attacking America's rule of law", Pompeo told reporters.
The head of State said he hopes to convince the ICC to change course in Afghanistan from taking action inconsistent with US views.
Pompeo went on to say, "this includes persons who take or have taken action to request or further section an investigation - these visa restrictions may also be used to deter ICC efforts to pursue ally personnel, including Israelis, without ally's consent".
"I'm announcing a policy of USA visa restrictions on those individuals directly responsible for any ICC investigation of U.S. personnel", the secretary of state said.
Pompeo made good on a threat delivered last September by President Donald Trump's national security adviser, John Bolton. Pompeo said Friday that more measures may come.
"While victims' rights should be the very top priority of the United States government, throwing roadblocks in front of the ICC's investigation undermines justice not only for abuses committed in Afghanistan, but also for the millions of victims and survivors throughout the world who have experienced the most serious crimes under worldwide law". Major powers, including the United States, China and Russian Federation, are not members.
Secretary of State Mike Pompeo said Washington was prepared to take further steps, including economic sanctions, if the war crimes court goes ahead with any probes of USA or allied personnel.
With 123 member states, including the entire European Union, the ICC was established in 2002 to prosecute war crimes, genocide or crimes against humanity when a country is unable or unwilling to prosecute perpetrators.
A State Department official said the United States would allow court officials to travel for meetings to the United Nations headquarters in NY.
Supporters of the court slammed Pompeo's announcement.
"The Trump administration is trying an end run around accountability", it said.
Richard Dicker, worldwide justice director at Human Rights Watch, said the USA move "is a naked attempt to bully judges and impede justice for victims in Afghanistan" and "blatant contempt for the rule of law".
The court has been hobbled by refusal of the U.S., Russia, China and other major nations to join.
"Taking action against those who work for the ICC sends a clear message to torturers and murderers alike: Their crimes may continue unchecked".
The American Civil Liberties Union, which represents three people before the ICC who say they were tortured in Afghanistan, called the decision "misguided and dangerous" and "an unprecedented attempt to skirt global accountability for well-documented war crimes that haunt our clients to this day".