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UPDATE 1-Tillerson to discuss North Korea crisis, trade in China

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WASHINGTON, Sept 26 (Reuters) - U.S. Secretary of State Rex Tillerson will visit China this week for talks that will include the crisis over North Korea's nuclear and missile programs and trade, the State Department said on Tuesday.

Tillerson's Sept. 28-30 trip would also lay the groundwork for U.S. President Donald Trump's visit to China in November, State Department spokeswoman Heather Nauert said.

Tillerson's visit comes at a time of high tension between the United States and North Korea, China's neighbor and ally, which is working to develop nuclear-tipped missiles capable of reaching the U.S. mainland.

President Donald Trump warned North Korea on Tuesday that any U.S. military option against North Korea would be "devastating" for Pyongyang, but said the use of force was not Washington's first option. China has urged a return to dialogue.

Nauert called China's steps to implement tougher U.N. sanctions on North Korea after its recent missile and nuclear tests "significant."

"We have a good relationship with China," she told a regular news briefing, adding that this was evidenced by what would be Tillerson's second visit to China in nine months in office.

"China has taken enormous steps in the right direction. There is always more that countries can do, but at this point we want to thank China for the steps it has taken in the right direction."

While backing U.N. sanctions, China, North Korea's main trading partner, opposes unilateral U.S. steps and has been worried Washington might move to freeze its banks out of the global financial system unless they cut all ties to Pyongyang.

On Tuesday, the U.S. Treasury announced sanctions against 26 more individuals as part of its non-proliferation designations for North Korea, as well as nine North Korean banks, including some with ties to China.

Tillerson's visit to Beijing will follow one by U.S. Commerce Secretary Wilbur Ross, who said on Monday China needed to guarantee fair and reciprocal treatment for U.S. firms, as he tried to strike an upbeat tone amid bilateral trade tensions.

China-U.S. ties have been strained by Trump's criticism of China's trade practices and by demands that Beijing do more on North Korea.

Chinese President Xi Jinping and Trump met for the first time at Trump's Mar-a-Lago estate in Florida in April. Trump has since played up his personal relationship with Xi, even while criticizing China over North Korea and trade.

In August, Trump authorized an inquiry into China's alleged theft of intellectual property - his first direct trade measure against Beijing, a move China called "irresponsible." (Reporting by David Brunnstrom; Editing by Andrew Hay and James Dalgleish)