* Trump cautions against "false hope" regarding Pyongyang
* North, South Korea to hold first summit since 2007
WASHINGTON/SEOUL, March 6 (Reuters) - U.S. President Donald Trump said on Tuesday he saw "possible progress" in denuclearization efforts with North Korea after South Korea said Pyongyang would be willing to meet with the United States and suspend nuclear tests while talks proceed.
The United States, South Korea and China responded with cautious optimism about North Korea's willingness to talk, a development that follows months of insults and threats of war between Trump and the North.
But some U.S. and South Korean officials said a breakthrough remained unlikely after the failure of previous talks, adding that North Korea may be trying to buy time to develop its weapons programs and seek relief from punishing American and U.N. sanctions.
"Possible progress being made in talks with North Korea," Trump wrote in a Twitter post. "For the first time in many years, a serious effort is being made by all parties concerned. The World is watching and waiting! May be false hope, but the U.S. is ready to go hard in either direction!"
There was no immediate comment from Pyongyang.
The news came as a South Korean delegation returned from a first-ever meeting with North Korean leader Kim Jong Un in Pyongyang on Monday.
The two sides will hold their first summit in more than a decade next month at the border village of Panmunjom, said Chung Eui-yong, the head of the South Korean delegation. The last inter-Korean summit was in 2007 when late former president Roh Moo-hyun was in office.
"North Korea made clear its willingness to denuclearize the Korean peninsula and the fact there is no reason for it to have a nuclear program if military threats against the North are resolved and its regime is secure," Chung told a media briefing.
Chung cited North Korea as saying it would not carry out nuclear or missile tests while talks with the international community were under way. North Korea has not carried out any such tests since last November. North Korea also is willing to discuss normalizing ties with the United States, Chung said.
North and South Korea are experiencing a significant easing in tensions since the Winter Olympics in the South last month, even though they are technically still at war because their 1950-53 conflict ended in a truce rather than a peace treaty.
China encouraged North and South Korea to continue their reconciliation efforts.
U.S. Vice President Mike Pence, who visited South Korea during the Olympics, said Washington will continue to apply "maximum pressure" on the North.
"All options are on the table and our posture toward the regime will not change until we see credible, verifiable, and concrete steps toward denuclearization," Pence said in a prepared statement.
Despite skepticism about Pyongyang's intentions, the prospect of talks nevertheless represents a significant potential development after heightened tensions and rhetoric between Kim and Trump, who last August threatened "fire and fury" if the North threatened the United States again.
Global stock markets rose on the news, with the broadest gauge of shares, MSCI's All Country World Index .MIWD00000PUS rising 0.5 percent.
North Korea has regularly vowed never to give up its nuclear program, which it sees as a "treasured sword" against the possibility of a U.S. invasion. The United States stations 28,500 troops in the south but denies any such plans.
In Washington, U.S. intelligence officials said it was too early to assess North Korea's willingness to consider denuclearization.
"Hope springs eternal but we need to learn a lot more relative to these talks. And we will," U.S. Director of National Intelligence Dan Coats told a Senate Armed Services hearing.
The director of the U.S. Defense Intelligence Agency, Lieutenant General Robert Ashley, told the same hearing that he did not share a sense of optimism, adding, "That's kind of a 'show me,' and so we'll see how this plays out."
Satellite images from last week indicate that North Korea may have resumed production of plutonium, presumably for its weapons program, according to 38 North, a Washington-based monitoring program.
Three U.S. officials who follow events on the Korean peninsula cautioned against getting too optimistic, saying there was no indication the North has abandoned its nuclear ambitions.
"We don't really have any choice but to welcome this development and take it seriously, but there also is every reason to hold our applause," one of the officials said.
(Additional reporting by Hyonhee Shin in Seoul, Ben Blanchard in Beijing and John Walcott, Matt Spetalnick, David Brunnstrom and Susan Heavey in Washington Writing by Andy Sullivan Editing by Yara Bayoumy and Will Dunham)