UPDATE 6-Seoul pushes for U.S.-Korea talks, Trump says 'We'll see'
* Moon says U.S., N.Korea should make concessions for talks
* "We'll see what happens," says Trump
* North and South Koreans meet for a second day
* Protesters angered by North Korean visit (Recasts)
SEOUL/WASHINGTON, Feb 26 (Reuters) - In the latest attempt to defuse the crisis over North Korea's weapons program, South Korea urged Washington and Pyongyang to give ground to allow for talks and U.S. President Donald Trump reiterated he would negotiate with North Korea, but only under the right conditions.
"Recently, North Korea has shown it is open to actively engaging the United States in talks and the United States is talking about the importance of dialog," South Korean President Moon Jae-in said during a meeting in Seoul with Chinese Vice Premier Liu Yandong.
"There is a need for the United States to lower the threshold for talks with North Korea, and North Korea should show it is willing to denuclearize. It's important the United States and North Korea sit down together quickly," he said, according to a statement from his office.
South Korea, a close U.S. ally, has engaged in a flurry of talks with North Korean officials since January, hoping to use the South's just-concluded Winter Olympics as a catalyst for rapprochement.
But the United States has insisted that any future talks with North Korea must be aimed at that country's denuclearization, something Pyongyang has rejected. North Korea on Sunday expressed willingness for dialog, Seoul says.
Trump, who has been pushing a global sanctions campaign against North Korea to force it to give up development of nuclear missiles capable of hitting the United States, reiterated that he would like to have talks with Pyongyang, but only if the conditions were right.
"They want to talk. We want to talk also, only under the right conditions. Otherwise we're not talking," Trump said while hosting a meeting with state governors at the White House.
"We'll see what happens. That's my attitude, we'll see what happens."
Trump and North Korean leader Kim Jong Un have exchanged taunts that have raised fears of war, and Trump last August threatened to go beyond sanctions by threatening "fire and fury" although his administration says it prefers a diplomatic solution to the crisis.
TRUMP'S 'PHASE TWO'
On Friday, Washington announced its largest package of sanctions yet on North Korea, and Trump warned of a "phase two" that could be "very, very unfortunate for the world" if the steps did not work - an apparent reference to military options his administration says remain on the table.
In another reference to the risk of war, Trump added on Monday: "We're talking about tremendous potential loss of lives, numbers that nobody's even contemplated, never thought of."
On Monday, Trump praised Chinese President Xi Jinping's support of U.N. sanctions and repeated accusations that Russia was stepping in to provide North Korea with items China used to provide.
"I think that President Xi is unique. He's helping us with North Korea," Trump said, crediting the relationship he has built up with the Chinese leader.
“And Russia is behaving badly because Russia is sending in what China is taking out. So China's doing pretty good numbers, but Russia is now sending a lot of stuff. But I think they want to see it come to an end also, I think everybody does."
North Korea has condemned the new sanctions and accused Washington of trying to undermine the improvement in inter-Korean relations.
NORTH KOREAN DELEGATION
A high-level delegation from North Korea has been visiting Seoul and meeting South Korean officials, including Moon, after attending the Olympics' closing ceremony on Sunday.
South Korea said the delegation told Moon that North Korea was open to talks with Washington.
The North Koreans attended a dinner hosted by Unification Minister Cho Myong-gyon, where participants agreed to keep working to boost inter-Korean ties.
Unification Ministry spokesman Baik Tae-hyun said he hoped constructive talks between North Korea and the United States could begin when "an appropriate opportunity" arose.
The North Korean delegation, led by former military intelligence chief Kim Yong Chol, met Chung Eui-yong, security adviser for the presidential Blue House, and other South Korean government officials for lunch on Monday.
Kim Yong Chol has been accused by South Korea of being behind the sinking of a South Korean warship in 2010 that killed 46 sailors and has been the subject of protests since his visit was announced. North Korea has denied the allegations.
"Both sides agreed to work together for permanent peace on the Korean peninsula, sustainable relations between North and South Korea and balanced cooperation with the international society," the South's presidential office said in a statement. (Reporting by Christine Kim in SEOUL and Roberta Rampton in WASHINGTON; Additional reporting by Doina Chiacu and David Brunnstrom; Editing by Jonathan Oatis)
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