South Korea has urged the North to give up its nuclear programme, after US officials said Pyongyang had admitted having atomic bombs.
The talks come amid rising tensions between the two Koreas
South Korea's delegates at high-level talks in Pyongyang said the North's possession of nuclear weapons would violate a bilateral agreement on a nuclear-free Korean peninsula.
The South Koreans say they pressed North Korean officials to confirm their alleged admission - reportedly made during talks with US officials in Beijing last week.
But the North Koreans declined to say whether they had nuclear weapons.
At the Beijing meeting last week, a senior American official said North Korea claimed to have atomic weapons that it might test, sell or use, depending on US actions.
During Sunday's meeting the head of the South Korean delegation, Unification Minister Jeong Se-hyun, said this was not acceptable to Seoul.
"We made it clear that we can never accept North Korea's possession of nuclear weapons," South Korean spokesman Shin Eun-sang said after the talks.
South Korean officials were tested for Sars after landing in Pyongyang
He added that this would constitute "a serious violation of the joint South-North declaration on denuclearisation".
The North's chief delegate, Kim Ryong-song, declined to comment on whether Pyonyang possesses nuclear weapons.
Instead, he reiterated that Pyongyang had made a "new bold proposal" at the Beijing talks.
The talks are due to continue until Tuesday
Earlier, North Korean medical officials checked the temperature of the South Korean delegates as a precautionary measure against Severe Acute Respiratory Syndrome (Sars).
The US envoy who says the North admitted possessing nuclear weapons, James Kelly, is now in Tokyo to brief Japanese officials on the outcome of the failed three-way meeting with the Chinese and North Koreans about the nuclear issue.
The White House said President George W Bush had spoken by telephone with Chinese Prime Minister Hu Jintao.
They discussed the goal of a Korean peninsula without nuclear weapons, and Mr Bush said he appreciated China's full and active participation in the talks.
The two Koreas promised to keep the peninsula nuclear-free in a 1992 agreement.
The US has said it is considering seeking UN sanctions against North Korea over the nuclear issue.
Oct 2002 - US says N Korea "admits" secret nuclear programme
Nov 2002 - US-led decision to halt oil shipments to N Korea
Dec 2002 - N Korea expels two nuclear watchdog's inspectors
Jan 2003 - N Korea says it is withdrawing from Nuclear Non-Proliferation Treaty
Feb 2003 - N Korea "restarts" Yongbyon nuclear plant
Apr 2003 - N Korea ends insistence on direct talks with US
Pyongyang has previously said it would consider sanctions a declaration of war.
In the US, officials said they would take a "good, hard look" at the North's alleged admission, to separate what they called "bluster" from reality. They said they still favoured reaching a diplomatic settlement over the issue.
The North has blamed the US for the collapse of the Beijing talks, saying it had provided a proposal but heard nothing new from the US.
South Korea and the US accuse North Korea of breaking a 1994 agreement, the Agreed Framework, in which the North agreed not to build nuclear weapons in exchange for the US construction of two "unweaponisable" light-water reactors.
The North counters that the light-water reactors, supposed to be due for completion in 2003, are years behind schedule.
It says its crippling power shortages are now forcing it to reconsider a nuclear programme.