South Korea on Tuesday responded to an overture from the North and proposed holding high-level talks between the countries on their border next week. North Korea’s leader, Kim Jong Un, had suggested on Monday that the countries open dialogue on easing military tensions and on the possibility of the North’s participating in the Winter Olympics in the South.

Cho Myoung-gyon, the South’s point man on the North, proposed that the Korean governments meet next Tuesday in Panmunjom, a village straddling the border north of Seoul, South Korea’a capital.

If the North responds positively, it will set in motion the first official dialogue between the Koreas in two years. South Korean officials hope the talks will lead to a thaw after years of high tensions between the countries and threats of war over the North’s pursuit of nuclear weapons.

But analysts cautioned that a sudden move to improve ties between the Koreas could strain relations between Seoul and Washington.

On Tuesday morning, President Trump responded on Twitter: “Sanctions and ‘other’ pressures are beginning to have a big impact on North Korea. Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not — we will see!”

Speaking at the United Nations on Tuesday, US Ambassador Nikki Haley appeared to dismiss the potential for bilateral negotiations between North and South Korea.

“We won’t take any of the talks seriously if they don’t do something to ban all nuclear weapons in North Korea,” she said. “We consider this to be a very reckless regime, we don’t think we need a Band-Aid; we don’t think we need to smile and take a picture. We think we need to have them stop nuclear weapons and they need to stop it now.”

Heather Nauert, State Department spokeswoman, said the Trump administration was still assessing whether the United States would support direct talks between South Korea and North Korea that excluded the United States.

“Right now, if the two countries decide that they want to have talks, that would certainly be their choice,” she said.

Nauert added that if Kim’s goal in proposing direct talks with the South was to divide the United States and South Korea, such a strategy would not succeed. “That will not happen,” she said.

Cho said the South was closely consulting with Washington on its dealings with the North.

Panmunjom has long been a contact point for the Koreas, with both sides exchanging messages through a telephone hot line there. But the North has not used the hot line since President Moon Jae-in’s conservative predecessor, the impeached President Park Geun-hye, shut down a joint industrial complex in the North Korean town of Kaesong in early 2016.

On Tuesday, Cho urged the North to restore the hot line so that both sides could discuss the agenda for the high-level talks. The governments held their last high-level dialogue in December 2015.

North Korea’s offer to send a delegation to the Winter Olympics, which are to begin in February in the South Korean town of Pyeongchang, represented a breakthrough for Moon, a dogged champion of dialogue and reconciliation with the North.

Moon has repeatedly urged North Korea to join the Pyeongchang Olympics, hoping it would ease the military tensions over the North’s nuclear and missile programs. Moon said the North’s participation would compel the Koreas to open talks, which he hoped would lead to broader negotiations, involving Washington and others, for the North’s denuclearization.

After ignoring Moon for months, calling his South Korean government a US stooge, Kim used his New Year’s speech Monday to embrace the South Korean leader’s overture.

“I appreciate and welcome the North’s positive response to our proposal that the Pyeongchang Olympics should be used as a turning point in improving South-North relations and promoting peace,” Moon said early Tuesday, instructing his Cabinet to move swiftly to open dialogue with North Korea.

In June, Moon, whose election in May ended the years of conservative rule, said he hoped to see the national teams of the two Koreas march together again in Pyeongchang.

The coming talks with North Korea over its Olympic participation could be a testing ground for Kim’s intentions.

While proposing to send an Olympic delegation, Kim on Monday said South Korea should end its regular joint military exercises with the United States and stop letting the Americans bring bombers and other nuclear-capable military assets to the Korean Peninsula. Moon has suggested that South Korea and the United States postpone their joint military drills until after the Olympics.

Kim also demanded that South Korea stop aiding the US-led campaign to squeeze North Korea with sanctions. Instead, he said the South should work with the North to bring peace to the Korean Peninsula, while boasting that his nuclear weapons would prevent the United States from starting a new war in Korea.

Analysts said Kim was using the North’s Olympic participation to try to drive a wedge in the alliance between South Korea and the United States and between Moon and Trump. Trump has taken a much tougher stance against the North, focusing on pressure and sanctions and once dismissing Moon’s efforts for dialogue with the North as “appeasement.”

In an analysis of Kim’s speech, the South’s Unification Ministry said Kim was seeking an “exit” from harsh sanctions by cultivating ties with South Korea.