The measure places financial and visa restrictions on individuals and their families who assist in ICC investigations of American citizens or allies.
Trump signed the measure as Israeli Prime Minister Benjamin Netanyahu was visiting Washington.
Last November, the ICC issued an arrest warrant for Netanyahu over alleged war crimes in Gaza, which Israel denies. The ICC also issued a warrant for a Hamas commander.
The Netherlands, which hosts the court, said it "regrets" Trump's order.
"The court's work is essential in the fight against impunity," Dutch Foreign Minister Caspar Veldkamp said on X.
A White House memo circulated on Thursday accused the Hague-based ICC of creating a "shameful moral equivalency" between Hamas and Israel by issuing the warrants at the same time.
Trump's executive order said the ICC's recent actions "set a dangerous precedent" that endangered Americans by exposing them to "harassment, abuse and possible arrest".
"This malign conduct in turn threatens to infringe upon the sovereignty of the United States and undermines the critical national security and foreign policy work of the United States government and our allies, including Israel," the order said.
The US is not a member of the ICC and has repeatedly rejected any jurisdiction by the body over American officials or citizens.
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