Secretary of State Mike Pompeo said the U.S. is imposing visa restrictions against International Criminal Court officials, citing investigations by the ICC into the activities of Americans and their allies in Afghanistan.

Mr. Pompeo said the visa restrictions had begun, and he declined to provide details on the number or identities of the individuals affected. He warned that the U.S. is prepared to take additional steps, including economic sanctions, in an effort to head off what he called improper investigations.

The...