The key test will be the reaction of the Chinese. American officials will have a chance to find out next week: Secretary of State John Kerry and Treasury Secretary Jacob J. Lew are traveling to Beijing for the Strategic and Economic Dialogue, where the isolation of North Korea will be a major subject of discussion. China voted for the latest United Nations sanctions, but Beijing’s fears of provoking a collapse of North Korea’s government still outweigh its desire to rein in Mr. Kim’s government.

Underlying the financial action was the United States’ desire to respond to North Korea’s third nuclear weapons test, conducted in January, which the country said was its first test of a hydrogen bomb. (There is no evidence that it was, in fact, a hydrogen weapon, which increases the magnitude of the blast.) More recently Pyongyang has attempted, and failed, to launch a Musudan intermediate-range missile. It is based on an early Soviet model, which was launched from a submarine, but the repeated failures have embarrassed Mr. Kim and undermined his effort to convince the world that his nuclear missile program is steaming ahead quickly.

The bigger mystery is whether Mr. Kim is also trying to show that he can undermine the global financial system, his best way of getting back at the West and his Asian neighbors for their support of sanctions. Two cybersecurity firms identified Pyongyang as the culprit behind a series of cyberattacks against Asian banks, including the theft that spirited $81 million from the central bank of Bangladesh’s account at the Federal Reserve Bank of New York.

Private security researchers analyzing those thefts say that unique digital fingerprints in the attackers’ code match those of the code used in cyberattacks against Sony in 2014 and South Korean banks and broadcasting companies in 2013. The Sony hack destroyed 70 percent of the firm’s computers.

South Korea has blamed North Korea for the attacks on its firms. Elements of the code in those attacks closely track some of the code found in the more recent bank thefts.

Banks in the United States are already prohibited from doing business with financial institutions in North Korea. But the recommended rules would require them to perform additional due diligence to ensure they are not inadvertently transacting with North Korean financial institutions or the Pyongyang government through shell companies or other fictitious entities.