WASHINGTON—The Trump administration on Friday levied what it called its largest ever North Korea sanctions package, hitting dozens of shipping and trading companies as it seeks to shrivel foreign-currency revenues to the nuclear-armed regime.

The administration sanctioned nearly 60 companies and ships and one individual it says are helping North Korea evade an international ban on coal exports and restrictions on fuel imports. That trade has enabled leader Kim Jong Un’s regime as he pursues an intercontinental ballistic missile...