South Korea's president proposed small peace steps Wednesday with North Korea including a park on the tense border but said that the communist state had to give up its nuclear weapons.

A day after an air-tight show of unity with US President Barack Obama, President Park Geun-Hye vowed in an address to the US Congress that any fresh "provocations" by North Korea would be "met decisively."

But the newly elected president also said she hoped to build trust with North Korea, saying the Demilitarized Zone on the last Cold War frontier "must live up to its name -- a zone that strengthens peace, not undermines it."

"It is with this vision in mind that I hope to work toward an international park inside the DMZ. It will be a park that sends a message of peace to all of humanity," she said.

Park said that North Korea had to respond first to build trust, telling the joint meeting of the Senate and House of Representatives: "As we say in Korea, it takes two hands to clap."

But the South Korean leader said that she hoped to develop a broader peace initiative for Northeast Asia, where friction involving regional heavyweights China and Japan have also been on the rise.

"We cannot afford to put off a multilateral dialogue process in Northeast Asia. Together, the United States and other Northeast Asian partners could start with softer issues," she said.

Such cooperation could focus on environmental issues and disaster relief -- and eventually involve North Korea.

"If we start where our interests overlap, then later it will be easier to find common ground on the larger challenges," she said.

The most visible symbol of cooperation between North and South Korea -- the Kaesong industrial park inside the impoverished communist side -- has been suspended amid the democratic South's fears for its citizens' safety.

Before her election, Park said she would pursue a policy of "trustpolitik" of stabilizing relations with North Korea. But tensions soared even before she took office, with Pyongyang carrying out its third nuclear test days ahead of her inauguration.

In remarks apocalyptic even by North Korea's standards, young leader Kim Jong-Un threatened nuclear war against the United States and South Korea.

Friction has appeared to ebb in the past week, with a US defense official saying that North Korea moved from launch sites two mid-range Musudan missiles -- meaning, at least for now, that there would be no imminent launch.

Park stood by her and Obama's insistence against offering any concessions to end the latest crisis cycle, saying South Korea "will never accept a nuclear-armed North Korea."

South Korea "is backed by the might of our alliance. So long as this continues, you may rest assured -- no North Korean provocation can succeed," she said to one of the loudest ovations from US lawmakers.

Few anticipate breakthroughs with North Korea, but analysts saw Park's approach -- a firm stance alongside the United States, but a forward-looking openness to dialogue -- as an attempt to coax Pyongyang to change.

"There is a window for Park to take the lead with her trustpolitik initiative, and she frankly has more political space than there is here in Washington to engage in a useful discussion at this stage," said Scott Snyder, a senior fellow at the Council on Foreign Relations.

Park, the first woman leader in Northeast Asia and daughter of slain dictator Park Chung-Hee, has used the trip to show harmony with the United States on the 60th anniversary of the armistice that halted the Korean War.

Park later met business leaders to mark one year since a long-debated free trade agreement entered into force between South Korea and the United States.

Pointing to resilient financial markets, Park tried to reassure US companies that tensions with Pyongyang would not affect Asia's fourth largest economy.

"No North Korean threat can undermine the Korean economy when its fundamentals are as strong as they are," she told the US Chamber of Commerce.