South Korean President Moon Jae-in said on Wednesday that sanctions on North Korea will not be eased for the sake of a summit between the two sides.
South Korean officials met North Korean leader Kim Jong Un on Monday in the first such encounter of its kind and said he had expressed his willingness to denuclearise, if his country's security is assured.
And US President Donald Trump said North Korea seems "sincere" in its apparent willingness to suspend nuclear tests if it holds denuclearisation talks with the United States.
Meanwhile Chinese state media repeated Beijing's line that talks are the only way to end the nuclear standoff.
Tensions rose to the highest level in years over North Korea’s nuclear and missile programmes, which it pursues in defiance of UN Security Council resolutions, with shrill, bellicose rhetoric coming from both Mr Kim and Mr Trump.
North Korea has boasted of its plans to develop a nuclear-tipped missile capable of reaching the mainland United States. But fears of all-out war eased last month, coinciding with North Korea's participation in the Winter Olympics in the South.
"From looking at the news or Twitter, I believe President Trump is positive about the results of the North Korea visit (by South Korean officials)," Mr Moon told political party leaders.
"However, as this is just the beginning, I believe we are not at a situation yet where we can be optimistic."
Mr Moon added he had no plans for an easing of sanctions.
"Just because there are talks ongoing between North and South Korea doesn't mean international sanctions can be eased," said Mr Moon. "There cannot be an arbitrary easing of sanctions; we do not wish to do that and I tell you now it is impossible."
South Korea's goal was the denuclearisation of North Korea, nothing less, said Mr Moon in comments distributed by the Blue House.
"We cannot have things like the prevention of nuclear proliferation or a moratorium as a final goal," said Mr Moon.
North and South Korea are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty. The North defends its weapons programmes as necessary to counter US aggression. The South hosts 28,500 US troops, a legacy of the war.
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North and South next month will have the first meeting between their leaders since 2007 at the border village of Panmunjom, Chung Eui-yong, head of the South Korean delegation, said on Tuesday.
Leaders around the world have also met the apparent breakthrough with guarded optimism, wary of repeating past negotiations that failed to prevent Pyongyang from developing nuclear weapons and intercontinental ballistic missiles.
On-again off-again "six-party" talks, grouping the two Koreas, Japan, Russia and the United States and hosted by China, ended in failure in 2009, with North Korea criticising US aggression.
South Korean officials who met the North Korean leader will leave for Washington on Thursday. Mr Chung said he had a verbal message from Kim Jong Un that he will relay to US officials but it was unclear whether he would meet Mr Trump.
After returning from the United States, Mr Chung will visit China and Russia, while Suh Hoon, the head of South Korea's intelligence agency, will head to Japan to brief officials.
President Trump told reporters in the Oval Office the United States had "come a long way, at least rhetorically" with North Korea and "statements coming out of South Korea and North Korea have been very positive".
Asked if he had any preconditions for talks, Mr Trump said: "I don't want to talk about it. We're going to see what happens."
US Vice President Mike Pence said the United States would continue to apply "maximum pressure" on North Korea and that all options were "on the table" until Washington sees evidence Pyongyang is taking steps towards denuclearisation.
Keeping up the pressure, the US State Department said on Tuesday it had determined Pyongyang used the chemical warfare agent VX to assassinate Mr Kim's half-brother in Malaysia in 2017 and had imposed sanctions in response. This information had already come out in court in Malaysia.
Chinese state-run tabloid the Global Times published an editorial saying the Korean nuclear issue cannot be solved without China, Russia and the UN Security Council.
“The reality is that North Korea now has an intercontinental ballistic missile that can allegedly hit targets in the US,” the paper wrote. “No one can intimidate anyone. Negotiation is the only way out."