The prospect worries the Latvian government so much that it ranks cleaning up money laundering above other urgent tasks like fixing a broken health care system and improving substandard schools and universities.

“It’s a matter of the reputation of the country,” Janis Reirs, the finance minister, said in an interview. “That’s why we said this is priority No. 1 for our government.”

Foreign observers do not doubt Mr. Reirs’s sincerity, but they are skeptical that a small, relatively poor country like Latvia can win a battle that essentially pits it against Russian oligarchs and organized crime figures who have been known to meddle in local politics. The government is an unstable alliance of five center-right parties.

“The problem is that you have a number of Russian- and Ukrainian-owned banks in Latvia with owners of dubious origin,” said Anders Aslund, a former Swedish diplomat who is a Russia expert at the Atlantic Council in Washington. “These people are strong and skillful.”

A few people in Latvia have gotten rich helping criminals move their money into the mainstream financial system, but revelations about illicit activity corroded the country’s reputation as a stable member of the North Atlantic Treaty Organization and the eurozone. In the past year, credit has become scarcer and banking more difficult.

Deutsche Bank and other Western financial companies have severed their correspondent banking relationships with Latvian lenders, effectively cutting off direct access to dollars. Now, when Latvian banks need to do business in dollars, they must go through intermediate banks in places like Poland or Spain, a process that creates delays.