The nuclear activities have also affected South Korea's relations with both the United States and China.
South Korean President Moon Jae-in took office in May. At the time, Moon said he wanted to balance contacts with sanctions to lower tensions on the Korean peninsula. In comparison, U.S. President Donald Trump has supported using "maximum pressure" on North Korea through economic sanctions and the threat of military action.
Yet after the North's nuclear test this week, conservatives in South Korea have been criticizing Moon's call for talks. President Trump also criticized the policy, calling it unworkable "appeasement."
The Moon administration has attempted to play down differences with the United States over how to deal with the growing North Korean threat. It says the two allies continue to support the idea of denuclearization. But Moon has also come out strongly against taking any preventive military action against North Korea — one that could lead to war.
Bong Young-shik is with the Yonsei University Institute for North Korean Studies in Seoul. He says "President Trump might have felt frustration about a seemingly softer stance from the South Korean leadership, but at the same time the Trump administration also agrees that military options are way too risky."
This week Moon seemed to take a stronger stance and one closer to the Trump administration's position. On Tuesday, he voiced support for new sanctions that would cut off the money North Korea earns from foreign currency income and oil supplies.
"If North Korea doesn't stop its provocations, we could face an unpredictable situation in the future," Moon said. He made the comment on Wednesday at a meeting with Russian President Vladimir Putin in the Russian city of Vladivostok.
However, Russian and Chinese leaders might not support new sanctions that have proven to be ineffective in slowing North Korea's nuclear missile development program. Putin said North Koreans would "eat grass" rather than give in to outside pressure to disarm. He called for talks to settle the crisis.
But the North Koreans said the nuclear tests will continue. Han Tae Song, the North's ambassador to the United Nations in Geneva, noted Tuesday that more North Korean missiles and nuclear tests are planned.
但是朝鲜人声称核试验将会继续下去。朝鲜驻联合国大使Han Tae Song周二表示，朝鲜计划进行更多的导弹和核试验。
President Trump said over the weekend that he is considering withdrawing from the U.S. Free Trade Agreement (FTA) with South Korea. That could also create a problem in the security alliance to oppose North Korea's nuclear missile program.
Trump has repeatedly criticized the five-year-old FTA for creating a $27 billion U.S. trade deficit with South Korea last year.
Chinese concerns about anti-missile system
The possibility of increased U.S. tariffs comes at the same time the Moon administration is facing Chinese criticism for deploying the American THAAD missile defense system.
China strongly objects to the radar system, calling it a threat to the country's security. China had reportedly ordered informal restrictions on some South Korean imports and travel as retaliation.
I'm Jonathan Evans.