COPENHAGEN—A massive Russia-linked money laundering case swelled in scope Wednesday when Denmark’s largest bank said more than $230 billion in transactions flowed through its tiny Estonian branch, a disclosure accompanied by the resignation of the bank’s chief executive.

The sheer size of the cited sums—much larger than previously reported—points to Danske Bank being the nexus of a colossal pipeline for carrying illicit money out of Russia and other former Soviet states. It has drawn scrutiny from U.S. criminal investigators,...