Donald Trump has reacted cautiously to news that North Korea is willing to talk about giving up its nuclear weapons if it did not feel threatened.
The US president said “the statements coming out of South Korea and North Korea have been very positive”, but also said it might be a “false hope”.
South Korea earlier said the subject was raised when its officials met the North’s leader, Kim Jong-un, on Monday.
Seoul said Mr Kim was also open to US talks, and would pause weapons testing.
However previous talks with North Korea have come to nothing, and some US and South Korean officials have suggested the North may be trying to buy time to develop weapons programmes, and to seek relief from biting sanctions.
There has also been no immediate comment from Pyongyang itself.
Further news that the leaders of North and South Korea have also agreed to meet at a summit next month, came via the leader of the South’s delegation, Chung Eui-yong.
It would be the first such meeting for more than a decade and the first since Kim Jong-un took power in North Korea.
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What did President Trump say?
Speaking to reporters at Washington’s Oval Office, he said: “We have come certainly a long way, at least rhetorically, with North Korea.
“The statements coming out of South Korea and North Korea have been very positive. That would be a great thing for the world.”
The US leader also praised Pyongyang for its decision to take part in the Pyeongchang Olympics in South Korea.
But he earlier posted a cautious tweet, warning about a “false hope”.
Meanwhile, US Vice-President Mike Pence said: “Whichever direction talks with North Korea go, we will be firm in our resolve.
“The United States and our allies remain committed to applying maximum pressure on the Kim regime to end their nuclear program.
“All options are on the table and our posture toward the regime will not change until we see credible, verifiable, and concrete steps toward denuclearisation.”
Lt Gen Robert Ashley, who heads the US Defense Intelligence Agency, said he did not share optimism voiced in America, adding that “we’ll see how this plays out”.
The US has maintained that North Korean gestures of rapprochement would carry little weight without a commitment on nuclear weapons – particularly following last year’s nuclear and missile tests carried out by the North.
The South Korean delegation is expected to visit Washington later this week to brief US officials on their talks in the North.
Meanwhile, China’s foreign ministry said it hoped the Koreas could continue with efforts to advance reconciliation, Reuters news agency reported.
What is North Korea reported to have said?
A statement from the South Korea president’s office issued earlier on Tuesday said: “The North showed willingness on denuclearisation in the Korean Peninsula. If military threats to the North Korea decrease and regime safety is guaranteed, the North showed that it has no reason to retain nukes.”
The North’s KCNA news agency said Mr Kim had “warmly welcomed” the delegates and held an “openhearted talk” with them.
It said the dinner took place “in a warm atmosphere overflowing with compatriotic feelings”.
However, some critics have suspicions over North Korea’s intentions. In the past, they have failed to follow through on deals, notably an aid-for-disarmament agreement in 2005.
What happened at the Pyongyang dinner?
South Korean officials had a four-hour dinner with Kim Jong-un on Monday. Among the delegation were intelligence chief Suh Hoon and National Security Adviser Chung Eui-yong.
Pictures showed Mr Kim and visitors from the South smiling broadly around a dinner table.
Also present was Mr Kim’s wife, Ri Sol-ju, who rarely appears at official events, and his sister Kim Yo-jong, who was part of a North Korean delegation to the Pyeongchang Olympics.
The two sides appear to be aiming to capitalise on the reduced tensions after the Games, which saw the Koreas march together under one flag.
During their visit, the South’s officials also held a boardroom meeting and passed on a letter from South Korean President Moon Jae-in, in which he invited Mr Kim to attend further talks.
KCNA said Mr Kim had “exchanged views and made a satisfactory agreement” on the letter and gave orders for it to be acted on.
The South’s delegates returned to Seoul on Tuesday morning, the South Korean news agency Yonhap said.
Has this ever happened before?
These were the first officials from Seoul to meet Mr Kim since he came to power.
Kim Jong-un has met very few foreign officials since he became leader in 2011 and the last time envoys from the South visited Pyongyang was in 2007.
Two previous summits were held in 2000 and 2007, under South Korean presidents Kim Dae-jung and Roh Moo-hyun who met Kim’s father, Kim Jong-il.
The South’s officials have stressed the talks were only preliminary, but the parties had “somewhat shared” views on some issues.