By Hyonhee Shin and Susan Heavey

SEOUL/WASHINGTON (Reuters) - North Korea's Kim Jong Un has given his first time line for denuclearization, aiming for the end of U.S. President Donald Trump's first term, Seoul officials said on Thursday, prompting thanks from Trump who said they would "get it done together".

Kim and South Korean President Moon Jae-in will meet in Pyongyang on Sept. 18-20 for a third summit and discuss "practical measures" toward denuclearization, Moon's national security adviser, Chung Eui-yong, said a day after meeting Kim.

The summit could provide renewed momentum to talks over denuclearization between North Korea and the United States, after Trump canceled a visit to Pyongyang by Secretary of State Mike Pompeo last month citing lack of progress.

Kim told South Korean officials his faith in Trump was "unchanged" and that he wanted denuclearization of the Korean peninsula and an end to hostile relations with the United States before Trump's first term ends in early 2021, Chung said.

But there was no indication that Kim had offered concrete steps toward giving up his nuclear arsenal, something some U.S. officials have said privately they doubt he is willing to do.

"He particularly emphasized that he has never said anything negative about President Trump," Chung said.

Trump welcomed Kim's remarks in a trademark Tweet.

"Kim Jong Un of North Korea proclaims 'unwavering faith in President Trump.' Thank you to Chairman Kim. We will get it done together!" Trump wrote.

Trump had previously hailed his landmark June 12 summit with Kim as a success and said the North Korean nuclear threat was over, despite little evidence to back that assertion.

In previous, failed talks, North Korea has said it could consider giving up its nuclear program if the United States provided security guarantees by removing troops from South Korea and withdrawing its so-called nuclear umbrella of deterrence from the South and Japan.

U.S. officials involved in the latest negotiations have said North Korea has refused to even start discussions about defining denuclearization and has insisted the United States must first agree to simultaneous steps to reduce sanctions pressure.

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Some analysts suggested Kim was flattering Trump in hopes of dividing the president from advisers who have advocated a tougher U.S. stand.

"Kim just owns Trump. He knows his mark," Vipin Narang, a political scientist at the Massachusetts Institute of Technology who specializes in nuclear issues, said in a message on Twitter.

'ENORMOUS AMOUNT OF WORK TO DO'

Pompeo, on a trip to New Delhi, said there was still "an enormous amount of work to do" on the denuclearization issue.

He visited Pyongyang in July, after which North Korea accused him of making "unilateral and gangster-like demands for denuclearization".

Asked about U.S. intelligence that North Korea was still advancing its weapons programs, Pompeo noted Pyongyang had ceased its nuclear tests and test-firing missiles, which he said was a "good thing."

"But the work of convincing Chairman Kim to make this strategic shift that we've talked about for a brighter future for the people of North Korea continues," Pompeo said.

The State Department later said Pompeo was sending his newly appointed North Korea envoy, Stephen Biegun, to South Korea, China and Japan from Sept. 10-15.

Signaling that Washington's concerns extend beyond Pyongyang's nuclear program, the U.S. government on Thursday charged and sanctioned an alleged North Korean hacker over the 2017 global WannaCry ransomware cyberattack, the 2014 cyber assault on Sony Corp. and other "malign cyber activities."

Chung said Kim had stressed the need for the United States to reciprocate North Korea's initial moves, which have included dismantling a nuclear test site and a missile engine facility.

"We support progress in inter-Korean relations and President Moon’s statements that such progress must go hand-in-hand with denuclearization," a spokesperson for the White House National Security Council (NSC) said when asked about the meeting

North Korea's official KCNA news agency said Kim told the South's envoys that his "fixed stand" was to turn the Korean peninsula into "a cradle of peace without nuclear weapons, free from nuclear threat".

Chung said Kim showed "frustration over the doubt raised by some parts of the international community about his willingness to denuclearize, and asked us to convey his message to the United States".

"He expressed his strong will to carry out more proactive measures toward denuclearization if action is taken in response to the North's preemptive steps," Chung said.

Koh Yu-hwan, a professor of North Korean Studies at Dongguk University in Seoul, said: "Looks like Kim is trying to wash away worries that talks could stall or fail, knowing well that Washington is losing patience."

U.S. officials have previously said they have already made conciliatory gestures, such as suspending joint military exercises with South Korea.

During his meeting with Kim, Chung delivered a message from Trump and will relay comments from Kim to U.S. National Security Advisor John Bolton, Moon's spokesman, Kim Eui-kyeom, told reporters. Chung later spoke to Bolton, the NSC official said.

Trump spoke to Moon on the evening before Chung's trip and asked Moon to act as "chief negotiator" between Washington and Pyongyang, the spokesman said.

However, a three-way summit between Trump, Kim and Moon - an idea that South Korea has floated - is not expected on the sidelines of the U.N. General Assembly in New York this month, Chung said, suggesting that Kim is not likely to become the first North Korean leader to attend the gathering.

U.N. Secretary-General Antonio Guterres praised the Koreas for their trust-building efforts and expressed hope for further progress toward "complete and verifiable denuclearization," his spokesman said.

WHAT HAPPENS FIRST?

Kim and Trump held an unprecedented summit in Singapore in June, in which the North Korean leader made a broad, vague commitment to work toward denuclearization of the Korean peninsula. But negotiations have stalled, while signs North Korea has maintained work on its weapons have emerged.

Under discussion is whether North Korean denuclearization or declaring an end to the 1950-53 Korean War should come first.

The war ended with an armistice, not a peace treaty, meaning U.S.-led U.N. forces are technically still at war with the North.

"The United States shouldn't delay any further an end-of-war declaration, which the U.S. president promised at the Singapore summit," the North's official Rodong Sinmun newspaper said.

U.S. officials have said such a declaration could weaken North Korea's incentive for denuclearization, and create uncertainty about the purpose of 28,500 U.S. troops stationed in South Korea.

(Additional reporting by Cynthia Kim and Joyce Lee in SEOUL, Matt Spetalnick, John Walcott, Susan Heavey, Lesley Wroughton and Christopher Bing in WASHINGTON and Phil Stewart in NEW DELHI; Writing by Soyoung Kim; Editing by Nick Macfie and James Dalgleish)