* Pompeo says talks with Pyongyang will be difficult but worth it
* Japan and South Korea praise Pompeo efforts
* Pompeo tells Japan's PM he raised abductees issue with Pyongyang
* N.Korea accuses Pompeo of making 'gangster-like' demands
* Pompeo also raised issue of Japanese abducted by N.Korea
US Secretary of State Mike Pompeo brushed off North Korean accusations of "gangster-like" diplomacy during negotiations in Pyongyang, saying on Sunday he will pursue denuclearisation talks after meeting his Japanese and South Korean counterparts.
Pompeo said in Tokyo there was still a lot of work to do but he was confident North Korean leader Kim Jong Un would stick to a commitment to abandon nuclear weapons he made during a summit with US President Donald Trump in Singapore last month.
Pompeo's meeting with Japan's Minister of Foreign Affairs Taro Kono and South Korean Foreign Minister Kang Kyung-wha followed two days of talks in Pyongyang that ended on Saturday.
"When we spoke to them about denuclearisation, they did not push back," Pompeo told a news conference. "The road ahead will be difficult and challenging and we know that critics will try to minimise the work that we've achieved."
Pompeo spoke after North Korea said the two days of talks with America's top diplomat "brought us in a dangerous situation where we may be shaken in our unshakable will for denuclearisation, rather than consolidating trust between the DPRK and the US".
The statement, which referred to the North's formal name of the Democratic People's Republic of Korea (DPRK), was carried by the official KCNA news agency on Saturday soon after Pompeo left Pyongyang.
Kim made a broad commitment in Singapore to "work toward denuclearisation" but did not give details on how or when he would dismantle North Korea's nuclear programme. Trump in turn offered security guarantees to Pyongyang and pledged a halt to large-scale military drills with South Korea.
North Korea's latest comments, which came after Pompeo said talks had made progress, are a reminder of the difficulties that previous US administrations have had negotiating with the reclusive state and suggest Pyongyang may not agree to any rapid denuclearisation.
Leaked US intelligence findings concluded that North Korea does not intend to give up its nuclear programme completely.
Trump has vowed that North Korea will not be allowed to threaten the United States with its ballistic missiles and nuclear weapons. His meeting with Kim in Singapore came after months of often bitter rhetoric and threats.
Military danger remains
Pompeo said he did not meet Kim on his latest visit to Pyongyang, as he had done twice before.
Richard Haass, president of the Council on Foreign Relations, said on Twitter there was a danger military action could be called for because Trump might now claim he had tried diplomacy but was betrayed by Kim.
"But a rushed summit and demands that NK denuclearise in short order or else is not a serious test of diplomacy," Haass tweeted.
Japan's Kono thanked Pompeo and said the three allies had reaffirmed a commitment to keeping sanctions on North Korea until it abandoned nuclear weapons and ballistic missiles of all ranges.
"We confirmed that security assurances will be provided to North Korea as agreed in the summit. At the same time we have reaffirmed that the international community will continue to fully implement relevant UN Security Council resolutions," Kono said.
Japanese Prime Minister Shinzo Abe earlier heaped praise on Pompeo at his residence in Tokyo.
"I would like to pay my tribute to the strong leadership you have demonstrated in negotiating with North Korea," Abe told Pompeo. "This really shows the unwavering bond of the Japan-US alliance."
South Korea's Kang said her country did not believe the United States had weakened its demands on Pyongyang.
"Secretary Pompeo's visit to Pyongyang this time has taken the first steps," she said. "We expect this to be followed up by further constructive and productive negotiations."
Pompeo said on Twitter after he met Kono he was in Tokyo to discuss the US alliance with Japan and maintaining "maximum pressure" on North Korea, an expression Trump's administration had backed away from after the Singapore summit.
He said before leaving for Pyongyang he was seeking to "fill in" details on North Korea's commitments and maintain the momentum towards implementing the Singapore agreement between Trump and Kim.
US intelligence officials earlier told Reuters Pompeo wanted to agree on at least an initial list of nuclear sites and an inventory that could be checked against available intelligence.
Pompeo said in Tokyo: "There is still much work to do to establish what the precise timeline of the various events will be," Pompeo said in Tokyo.
He said he had also pushed North Korea on a promise to destroy a missile engine test site and that the United States would like that to happen "soon".
Pompeo said talks had yielded an agreement to form a "working level" group to oversee day-to-day interactions between the United States and North Korea.
Officials from the two sides would meet next week in Panmunjom, on the border between the two Koreas, to discuss the return of the remains of the some 7,000 US soldiers missing since the 1950-53 Korean War.
KCNA said Pyongyang had offered to discuss declaring a formal end to the 1950-53 Korean War to mark next month's anniversary of the armistice agreement. It said the US side had shown little interest, giving "certain conditions and excuses".
Pompeo also told Abe he had raised the issue of Japanese people abducted by North Korean agents in the 1960s and 1970s to train its spies.
In addition to demanding that North Korea agree to the complete, verifiable and irreversible abandonment of its nuclear weapons and missile programmes, Abe has made the return of any abductees still in North Korea or a full disclosure of their fates a condition for providing any major economic assistance.
Pompeo also met South Korea's Kang separately in Tokyo before leaving for Vietnam on the next leg of his trip through Asia and Europe. They discussed inter-Korean relations, peace and complete denuclearisation of the Korean peninsula, the South Korean government said in a statement.