North Korea says it put forward a "bold proposal" at talks on its nuclear programme, but heard nothing new from the United States.
South Korea is keeping a close eye on the North
The foreign ministry in Pyongyang accused the Americans of avoiding essential issues - but gave no details of its own offer.
The talks in Beijing ended amid mutual recriminations on Friday, after US officials said Pyongyang had admitted having nuclear weapons.
President George W Bush earlier accused North Korea of using "blackmail", after the new claims about its nuclear programme emerged in Washington.
US Secretary of State Colin Powell said "strong views" were expressed - which the BBC's State Department correspondent Jon Leyne says is barely coded diplomatic parlance for a blazing row.
A North Korean foreign ministry spokesman said the US had "repeated its old assertion that the DPRK (North Korea) should 'scrap its nuclear programme before dialogue,' without advancing any new proposal".
The spokesman added that American officials had "persistently avoided the discussion on the essential issues to be discussed between both sides".
The DPRK set out a new proposal for the settlement of the nuclear issue, proceeding from its stand to avert a war on the Korean peninsula
North Korea did not comment on the alleged admission that it possesses nuclear weapons. In the past it has denied similar US reports, merely stating it has "the right" to have such weapons.
The BBC's Caroline Gluck in Seoul says the talks may have only succeeded in emphasising the gulf in positions between Washington and Pyongyang rather than narrowing them.
However Chinese officials described the three-way discussions as "a good start" and said all sides had agreed to keep diplomatic channels open.
Russia, for its part, urged North Korea and the US to "continue the search for a negotiated settlement".
The US Assistant Secretary of State for East Asian Affairs, James Kelly, has flown to Seoul to brief South Korean officials about the talks in Beijing. He is due to travel to Japan on Saturday.
South Korea's Foreign Minister Yoon Young-kwan, speaking after meeting Mr Kelly, said: "If it is true that North Korea possesses nuclear weapons, this would be a major breach of peace on the Korean peninsula".
On Thursday Mr Powell warned Pyongyang that the US would not give in to threats.
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
"The North Koreans should not leave the meetings... with the slightest impression that the United States or its partners will be intimidated by bellicose statements or threats," he said.
He added that the US was not taking "any options off the table" - a hint that Washington might use military force.
Wendy Sherman, a special adviser on North Korea to former US President Bill Clinton, warned that Pyongyang does not limit itself to making threats.
"North Korea turns threats into actions, so the stakes are very high," she told the BBC.
North Korea's alleged claim that it had nuclear weapons will send shock waves through the region, the BBC's Charles Scanlon in Tokyo says.
The South Korean stock market and currency fell sharply following the statement. Japan will also be alarmed at the possible implications, our correspondent adds.
It is not clear exactly what the North Koreans said to the US delegation.
According to US media reports, the head of the North Korean delegation pulled aside his opposite number and said that the North possessed nuclear weapons and it was up to the US whether the North did a "physical demonstration" or transferred them.
US media also said that the North had claimed to have nearly finished reprocessing 8,000 spent nuclear fuel rods, which, if true, would allow the country to add to its nuclear arsenal.
Sources inside the Bush administration denied being surprised by North Korea's claim to have nuclear weapons as it merely confirmed US intelligence suspicions.
However, the claim about the fuel rods was surprising since Western and Asian intelligence services believed reprocessing was not yet underway.
The US wants to persuade North Korea to close down its nuclear programmes, while the North wants assurances the US will not attack.
The last time Mr Kelly held talks with a North Korean delegation, he accused them of pursuing a clandestine nuclear weapons programme, sparking the crisis in October.
North Korea's fuel rods could be used to make nuclear bombs
President Bush later suspended oil aid shipments under a 1994 agreement designed to prevent Pyongyang from developing nuclear weapons.
In December, North Korea restarted its nuclear facilities, expelled United Nations inspectors and withdrew from the Nuclear Non-Proliferation Treaty (NPT).