Chinese banks and other financial entities have been a lifeline for the regime of North Korean leader Kim Jong Un, and although China has cut many ties and helped impose international sanctions, U.S. officials say cracks remain.

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Just before Trump spoke in the Rose Garden, the Treasury Department announced new sanctions on eight North Korean banks and 26 people in China, and three other countries that the Trump administration says are linked to North Korean financial networks.

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“North Korean nuclear weapons and missile development threaten the entire world with unthinkable loss of life,” Trump said. “All nations must act now to ensure the regime's complete denuclearization.”

The rhetoric was mild in comparison with Trump's vow last week to “totally destroy” North Korea, if necessary, and his derisive reference to Kim as “Rocket Man.”

Kim, in turn, had called Trump “deranged” and possibly senile, and the North Korean foreign minister said Monday that Trump's words amounted to a declaration of war.

The Trump administration says its policy of international pressure is starting to work. The goal is to persuade Kim to give up the nuclear weapons he claims he needs to ensure his security against a U.S. attack. China is the linchpin, as Beijing is both North Korea's main economic partner and its traditional protector.

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The State Department announced Tuesday that Secretary of State Rex Tillerson will visit China next week to discuss North Korea as well as to plan for Trump's visit to China later this year.

The United States has led a pressure campaign to get other nations to stop doing even minimal trade or banking business with North Korea, and to cut or downgrade diplomatic relations with Pyongyang. Those efforts are on top of tighter economic penalties imposed at the United Nations over the last two months.

“I appreciate the United Nations Security Council voting twice, unanimously — 15 to nothing, twice — to adopt hard-hitting resolutions against North Korea,” Trump said Tuesday. “I have recently issued tough new sanctions against those who do business with this outlaw regime. And I applaud China's latest action to restrict its trade with North Korea.”