U.S. Secretary of State Rex Tillerson is making his second trip to China since taking office in February, and relations between the two world powers have rarely mattered so much.
 
   The standoff over North Korea's nuclear weapons has entered a new, dangerous phase as its leader, Kim Jong Un, and President Donald Trump exchange personal insults and threats of war with no sign of a diplomatic solution.
 
   Even as Washington and Beijing grapple with that security crisis, Trump wants action from China for more balanced trade with America -- a dispute with ramifications for the global economy.
 
   Tillerson, facing criticism at home for his muted impact as the top U.S. diplomat, will be laying the groundwork for Trump's planned visit to China in November. He meets Saturday with Chinese Foreign Minister Wang Yi and other Chinese leaders.
 

   What will be on the agenda:
 
   NORTH KOREA
 
   Tillerson will be pushing China to fully implement the latest U.N. Security Council resolutions on North Korea and take further steps on limiting crucial oil supplies to its troublesome neighbor. If the restrictions on trade in textiles, coal and other commodities are properly enforced, North Korea will lose the vast majority of its export revenue. In its latest step to comply with the sanctions, China on Thursday ordered North Korean-owned businesses to close by early January.
 
   China accounts for about 90 percent of North Korea's foreign trade, so it's pivotal in the U.S.-led campaign to exert economic pressure with the aim of getting the pariah nation to disarm. State Department spokeswoman Heather Nauert said Tuesday that "China has taken tremendous steps in the right direction.'' Trump has also lauded an order by China for its banks to stop dealing with North Korea, although Beijing has yet to announce such a measure.
 
   But U.S. praise always comes with a proviso: that China needs to do more. There's a growing sense of urgency. North Korea is moving closer to its goal of having a nuclear-tipped missile that could strike America. Yet Beijing remains skeptical about the efficacy of sanctions and wary of drastic action that could cause North Korea to collapse. China wants the U.S. to restart dialogue with Pyongyang. That's an increasingly distant prospect after the recent angry exchanges between Trump and Kim.
 
   TRUMP VISIT
 
   China doesn't want Tillerson's visit to be consumed by North Korea. It wants attention paid to Trump's state visit in November.
 
   Stewardship of the U.S. relationship is crucial for the standing of any Chinese leader. It will be Trump's first trip to Asia and it will come just weeks after Xi Jinping is due to be anointed with a second five-year term as the leader of China's communist party.
 
   Despite his tough criticism of China's trade practices, Trump has forged a personal connection with Xi. He hosted the Chinese president at his Mar-a-Lago resort in April, where they agreed on four high-level dialogues to cover various aspects of relations. In a prelude to his trip to Beijing, Trump met Thursday with Chinese Vice Premier Liu Yandong, who was attending the inaugural dialogue on people-to-people ties in Washington.
 
   The November meeting of the two leaders will be grander and more choreographed than the informal talks in Florida that were most memorable for Trump's ordering a missile strike on Syria and then informing Xi about it afterward over dinner as they ate chocolate cake.
 
   Other than North Korea, the U.S. and China have other security concerns to address. They remain at odds over Beijing's military buildup and assertive claims to disputed islands in the South China Sea.
 
   TRADE AND INVESTMENT
 
   Trump has slammed China's large trade surpluses with the United States and last month ordered an investigation into whether Beijing improperly pressures companies to hand over their technology in exchange for market access. Last year, the U.S. ran up a $347 billion trade deficit in goods with China _ accounting for nearly half the total.
 
   During the Mar-a-Lago summit, the two leaders agreed on a 100-day plan for trade talks. After visiting China this week, U.S. Commerce Secretary Wilbur Ross said there's been some progress, including a deal to let U.S. beef into China, but they need to tackle ``bigger things and more difficult things.'' The U.S. priorities are better market access, less protectionism and protecting intellectual property rights.
 
   In Beijing this weekend, Tillerson is likely to restate those U.S. concerns and raise the impact of national security legislation on American companies operating in China. Washington wants Beijing to make good on its promise to let market forces have a bigger role in its economy, give equal treatment to foreign and Chinese companies and roll back state industry's dominance.