The measure is not expected to become law, but it reflects continued support for Israel in Congress amid international criticism over the Middle Eastern country's operations in the Gaza Strip.
Last month, the White House criticized the ICC's decision to seek the warrant.
The bill is not expected to come to a vote in the Senate, which Biden’s fellow Democrats have narrow control over.
The bill would ban those who are prosecuted by the ICC from being Americans or citizens of non-ICC member countries (including Israel).