By Ben Blanchard

BEIJING (Reuters) - China on Wednesday urged all parties in the Korean standoff to stay calm and "stop irritating each other," a day after North Korea said the United States was pushing the region to the brink of nuclear war.

North Korea's state media published a rare, strong, criticism of China on Wednesday, saying Chinese state media commentaries calling for tougher sanctions over Pyongyang's nuclear program were undermining relations with Beijing and worsening tensions. {nL8N1I55TR]

The United States has urged China, North Korea's only major ally, to do more to rein in its neighbor's nuclear and missile programs, which have prompted an assertive response from the Trump administration, warning that an "era of strategic patience" is over.

U.S. Secretary of State Rex Tillerson said on Wednesday that Washington was working on more sanctions against North Korea if Pyongyang takes steps that merit a new response. He also warned other countries their firms could face so-called secondary sanctions for doing illicit business with Pyongyang.

Tillerson said the Trump administration had been "leaning hard into China ... to test their willingness to use their influence, their engagement with the regime."

Diplomats said this week Washington was negotiating with China on a possible stronger U.N. Security Council response - such as new sanctions - to North Korea's missile tests.

Chinese Foreign Ministry spokesman Geng Shuang said on Wednesday U.N. resolutions were clear that further measures would be taken in the event of more nuclear or missile tests.

The United States has sent a nuclear-powered aircraft carrier to Korean waters and a pair of strategic U.S. bombers flew training drills with South Korea and Japan in another show of strength this week.

Chinese Foreign Ministry spokesman Geng Shuang called the situation "highly complex" and sensitive.

"The urgent task is to lower temperatures and resume talks," he said.

"We again urge all relevant parties to remain calm and exercise restraint, stop irritating each other, work hard to create an atmosphere for contact and dialogue between all sides, and seek a return to the correct path of dialogue and negotiation as soon as possible."

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The bomber flights coincided with U.S. President Donald Trump raising eyebrows when he said he would be "honored" to meet North Korean leader Kim Jong Un in the right circumstances, and as his CIA director landed in South Korea for talks.

North Korea said the bombers conducted "a nuclear bomb dropping drill against major objects" in its territory at a time when Trump and "other U.S. warmongers are crying out for making a preemptive nuclear strike."

"The reckless military provocation is pushing the situation on the Korean peninsula closer to the brink of nuclear war," North Korea's official KCNA news agency said.

A commentary on KCNA on Wednesday took aim at China and state media articles it said had attempted to shift the blame to Pyongyang for "deteriorated relations" between China and North Korea and U.S. deployment of strategic assets.

It also accused China of "hyping up" damage caused by North Korean nuclear tests to China's three northeastern provinces and said the program was needed for the "existence and development" of the country and "can never be changed nor shaken."

Tension on the Korean peninsula has been high for weeks, driven by concern that North Korea might conduct its sixth nuclear test in defiance of U.N. Security Council resolutions.

CHINA OPPOSES THAAD

U.S. officials told Reuters the U.S. military's THAAD anti-missile defence system had reached initial operational capacity in South Korea, although it would not be fully operational for some months.

China has repeatedly expressed its opposition to the system, whose powerful radar it says can reach inside Chinese territory, even as Trump has praised Chinese President Xi Jinping for his efforts to rein in North Korea.

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Trump has urged other Asian countries to help pressure North Korea and spoke last weekend with the leaders of Thailand, Singapore and the Philippines.

He drew criticism on Monday when he said he would be "honored" to meet North Korea's young leader.

"If it would be appropriate for me to meet with him, I would absolutely, I would be honored to do it," Trump told Bloomberg News.

Trump did not say what conditions would be needed for such a meeting or when it could happen, but White House spokesman Sean Spicer said "clearly conditions are not there right now."

Washington has said any future talks on North Korea must based on its willingness to abandon its nuclear weapons program.

Trump warned in an interview with Reuters on Thursday a "major, major conflict" with North Korea was possible, while China has said the Korean situation could slip out of control.

In a telephone call with his Philippine counterpart Rodrigo Duterte, Xi urged all sides to return to talks as soon as possible, Chinese state radio reported.

North Korea on Saturday conducted its fourth successive failed missile launch since March. It has conducted two nuclear tests and dozens of missile tests since the beginning of 2016.

The U.S. ambassador to Indonesia, Joseph R. Donovan, told reporters Indonesia was among several countries Washington was urging to take a "fresh look" at their North Korea ties.

Trump also spoke on Tuesday with Russian President Vladimir Putin and discussed "how best to resolve the very dangerous situation in North Korea", the White House said.

(Additional reporting by David Brunnstrom, Yeganeh Torbati and Steve Holland in WASHINGTON and Tom Allard in JAKARTA; Writing by Nick Macfie and David Brunnstrom; Editing by Robert Birsel and Grant McCool)