The Treasury Department plans to sever ties between one the Baltic’s largest banks and U.S. markets, charging the institution with laundering billions of dollars in illicit funds, including for companies connected to North Korea’s banned ballistic-missile program, the Trump administration said.

The rarely used action, part of a broader pressure campaign against North Korea and Russia, is one of Treasury’s most powerful tools. Tuesday’s sanction makes Latvia-based ABLV Bank, which is based in Riga but has an office in Luxembourg...