* N.Korea says no need for nuclear programme if regime secure
* N.Korea says open to denuclearization talks with U.S. - South
* Trump sees "possible progress" on talks (Adds further Trump tweets, updates markets)
SEOUL, March 6 (Reuters) - North Korea is willing to hold talks with the United States on denuclearization and will suspend nuclear tests while those discussions are under way, the South said on Tuesday after a delegation returned from meeting the North's leader Kim Jong Un.
Responding to the news in a series of tweets, U.S. President Donald Trump said he saw "possible progress" and that "for the first time in many years, a serious effort is being made by all parties concerned".
The potential talks "may be false hope, but the U.S. is ready to go hard in either direction," Trump tweeted.
There was no immediate comment from Pyongyang.
"North Korea made clear its willingness to denuclearize the Korean peninsula and the fact there is no reason for it to have a nuclear programme if military threats against the North are resolved and its regime is secure," the head of the South Korean delegation, Chung Eui-yong, told a media briefing.
North and South Korea, still technically at war but enjoying a significant easing in tension since the Winter Olympics in the South last month, will also hold their first summit in more than a decade next month at the border village of Panmunjom, Chung said.
Chung cited the North 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 November last year.
"The North also said it can have frank talks with the United States on denuclearization and the normalisation of ties between North Korea and the United States," Chung said.
The prospect of talks between the isolated North and the United States helped boost global stock markets, with the broadest gauge of global shares, MSCI's All Country World Index , rising 0.7 percent and Wall Street stocks opening higher .
Washington and Pyongyang have been at loggerheads for months over the North's nuclear and missile programmes, with Trump and Kim Jong Un trading insults and threatening war. North Korea has regularly vowed never to give up its nuclear programme, which it sees as an essential deterrent and "treasured sword" against U.S. plans for invasion.
The United States, which stations 28,500 troops in the South, a legacy of the Korean War, denies any such plans.
The U.S. Director of National Intelligence, Dan Coats, said that Washington would have to know far more before assessing North Korea's reported willingness to discuss denuclearization.
"Hope springs eternal, but we need to learn a lot more relative to these talks," Coats told the U.S. Senate Armed Services hearing on Worldwide Threats on Tuesday.
To ensure close communication, the two Koreas, whose 1950-53 conflict ended in a truce rather than a peace treaty, will set up a hotline between South Korean President Moon Jae-in and Kim Jong Un, Chung said.
The last inter-Korean summit was in 2007 when late former president Roh Moo-hyun was in office.
The agreement came on the heels of a visit made by a 10-member South Korean delegation led by Chung to the North Korean capital, Pyongyang, on Monday.
Kim Jong Un met senior South Korean government officials for the first time and said it was his "firm will to vigorously advance" inter-Korean ties and pursue reunification, the North's official news agency said earlier.
Tensions between the two Koreas eased during the Olympics in South Korea, where Moon hosted a high-level North Korean delegation and the two sides presented a joint women's ice hockey team. Kim Jong Un had invited Moon to North Korea for a summit, which was the first such request from a North Korean leader to a South Korean president.
U.S.-S.KOREA DRILLS TO GO ON
North Korea has boasted of developing nuclear-tipped missiles capable of reaching the United States, in defiance of U.N. Security Council resolutions, but Pyongyang and Washington both say they want a diplomatic solution to the stand-off.
The first inter-Korean talks in more than two years were held early this year to bring North Korea to the Winter Olympics, when South Korea and the United States also postponed an annual joint large-scale military exercise that North Korea views as a preparation for invasion.
During this week's visit, a senior Blue House official said North Korea was informed it was not feasible to postpone the joint military drills between South Korea and the United States again and that Kim Jong Un acknowledged the situation.
Kim Jong Un said he understood the drills, expected in April, would be of a similar scale seen in previous years, the official said. The North Korean leader also had a request for the world: that he be seriously acknowledged as a dialogue counterpart, said the official.
The South's delegation leader, Chung, said he would travel to the United States to explain the outcome of the visit to North Korea and that he had a message from North Korea he would deliver to Trump.
Chung will later visit China and Russia, while Suh Hoon, the head of South Korea's spy agency and another member of the delegation, will head to Japan.
The United States has said before it is open to talks but its position has been that dialogue must be aimed at North Korea's denuclearization, something Pyongyang has rejected.
Moon has also remained vigilant against North Korea's weapons ambitions, saying on Tuesday South Korea should bolster its defences in tandem with talks with Pyongyang. (Reporting by Christine Kim Additional reporting by Hyonhee Shin Editing by Alex Richardson and John Stonestreet)