Pompeo, speaking from the State Department Friday, said the restrictions include "persons who take or have taken action to request or further such an investigation".
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.
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.
ICC prosecutor Fatou Bensouda announced the investigation two years ago and said it's looking for evidence of war crimes, like torture, that were committed by military personnel in Afghanistan since 2001.
Nevertheless, Human Rights Watch was not happy by the Trump Admsinstatrion's latest move, calling it "thuggish".
Pompeo made good on a threat delivered last September by US President Donald Trump's national security adviser, John Bolton.
Pompeo's announcement of visa restrictions was the first concrete action taken by the United States against the ICC since the White House threatened reprisals against the Hague-based body in September of previous year.
Pompeo slammed the potential investigation an example of "politically motivated prosecutions of Americans".
In November 2017, ICC prosecutor Fatou Bensouda announced that she would ask judges for permission to open an investigation into alleged war crimes committed in the Afghan conflict, including by the United States military.
"That the administration has chosen visa bans, powerful tools typically reserved for the most serious of human rights abusers, to prevent investigation into allegations involving some of the most serious crimes in the world is highly indicative of its culture of disregard for rights abuses".
"We will not cooperate with the ICC". In 2002, Bolton, then a State Department official, traveled to NY to ceremonially "unsign" the Rome Statute at the United Nations.
Al Jazeera's Patty Culhane, reporting from Washington, said ICC investigators were also seeking to probe the United States 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".
"The court is an independent and impartial judicial institution crucial for ensuring accountability for the gravest crimes under global law", the statement said.
"These visa restrictions will not be the end of our efforts", he said.
The International Criminal Court is supported by 123 nations, including Switzerland. Major powers, including the United States, China and Russian Federation, are not members.
"Taking action against those who work for the ICC sends a clear message to torturers and murderers alike: Their crimes may continue unchecked", she said, and called on U.S. lawmakers to rescind the move and express support for the court.
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