WASHINGTON/MOSCOW (Reuters) - U.S. President Donald Trump dismissed a Chinese diplomatic effort to rein in North Korea’s weapons program as a failure on Thursday, while Secretary of State Rex Tillerson said Beijing was doing a lot, but could do more to limit oil supplies to Pyongyang.

In a tweet, Trump delivered another insulting barb against North Korean leader Kim Jong Un, who he called “Little Rocket Man” and a “sick puppy” after North Korea test-fired its most advanced missile to date on Wednesday.

Russian Foreign Minister Sergei Lavrov said Washington’s approach was dangerously provocative.

Trump’s tweets further inflamed tensions reignited this week after North Korea said it had successfully tested a new intercontinental ballistic missile in a “breakthrough” that put the U.S. mainland within range of its nuclear weapons whose warheads could withstand re-entry to the Earth’s atmosphere.

“The Chinese envoy, who just returned from North Korea, seems to have had no impact on Little Rocket Man,” Trump said on Twitter, a day after speaking with Chinese President Chinese President Xi Jinping and reiterating his call for Beijing to use its leverage against North Korea.

Tillerson on Thursday welcomed Chinese efforts on North Korea, but said Beijing could do more to limit its oil exports to the country.

“The Chinese are doing a lot. We do think they could do more with the oil. We’re really asking them to please restrain more of the oil, not cut it off completely,” Tillerson said at the State Department. China is North Korea’s neighbor and its sole major trading partner.

While Trump has been bellicose at times in rhetoric toward North Korea, Tillerson has persistently held out hopes for a return to dialogue if North Korea shows it is willing to give up its nuclear weapons program.

However, Tillerson may not remain in his job long, with disagreements with Trump over North Korea being one factor. On Thursday, senior Trump administration officials said the White House was considering a plan to replace Tillerson with Mike Pompeo, the director of the Central Intelligence Agency.

U.S. Defense Secretary Jim Mattis said he still had confidence in diplomatic efforts on North Korea and that the United States would be “unrelenting” in working through the United Nations.

In spite of Trump’s rhetoric and warnings that all options, including military ones, are on the table in dealing with North Korea, his administration has stressed it favors a diplomatic solution to the crisis.

Trump has pledged more sanctions in response to the latest test and, at an emergency U.N. Security Council meeting late Wednesday, the United States warned North Korea’s leadership would be “utterly destroyed” if war were to break out.

“This administration is focused on one big thing when it comes to North Korea, and that’s denuclearization of the Korean peninsula,” White House spokeswoman Sarah Sanders told a regular White House briefing.

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“Anything beyond that is not the priority at this point,” she said, responding to a question on whether regime change was on the administration’s agenda after Trump’s recent tweets and a speech by U.N. Ambassador Nikki Haley.

LAVROV REJECTS U.S. CALL

Lavrov pointed to joint U.S.-South Korean military exercises planned for December and accused the United States of trying to provoke Kim into “flying off the handle” over his missile program to hand Washington a pretext to destroy his country.

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He also flatly rejected a U.S. call for Russia to cut ties with Pyongyang over its nuclear and ballistic missile program, calling U.S. policy toward North Korea deeply flawed.

In a call with Trump on Thursday, South Korean President Moon Jae-in said the missile launched this week was North Korea’s most advanced so far, but it was unclear whether Pyongyang had the technology to miniaturize a nuclear warhead and it still needed to prove other things, such as its re-entry technology.

A White House statement said Trump and Moon reiterated their strong commitment to enhancing the deterrence and defense capabilities of the U.S.-South Korea alliance and added: “Both leaders reaffirmed their strong commitment to compelling North Korea to return to the path of denuclearization at any cost.”

North Korea has tested dozens of ballistic missiles under Kim’s leadership and conducted its sixth and largest nuclear bomb test in September.

It has said its weapons programs are a necessary defense against U.S. plans to invade. The United States, which has 28,500 troops in South Korea as a legacy of the 1950-53 Korean War, denies any such intention.

Previous U.S. administrations have failed to stop North Korea from developing nuclear weapons and a sophisticated missile program. Trump, who has previously said the United States would “totally destroy” North Korea if necessary to protect itself and its allies from the nuclear threat, has also struggled to contain Pyongyang since taking office in January.