The US has said it hopes to persuade North Korea to return to multi-party talks on its nuclear weapons programme, but it ruled out offering concessions.
North Korea is believed to have built a handful of nuclear weapons
Washington also played down the significance of Pyongyang's public claim that it has nuclear weapons.
White House spokesman Scott McClellan said the US remained "committed to a peaceful diplomatic solution".
Pyongyang has said it is quitting talks indefinitely, declaring them pointless because of "hostile" US policy.
Deputy state department spokesman Adam Ereli said the US had long assumed that North Korea had a nuclear capability, and stressed the importance of the six-party talks.
However, he ruled out offering North Korea new incentives to return to the negotiations.
"Our position is consistent, and we don't see a need to review it," he said.
World leaders have criticised North Korea's decision to pull out of the talks.
South Korea, China and Russia - other members of the six-party talks that also include Japan - urged Pyongyang to reconsider.
A senior South Korea official said: "We make it clear that we won't tolerate the North's nuclear weapons."
US Secretary of State Condoleezza Rice said Pyongyang risked deepening its isolation.
"The world has given them a way out and we hope they will take that way out," she said in Luxembourg.
US RHETORIC ON NORTH
19 Jan: Condoleezza Rice refers to North as an "outpost of tyranny"
20 Jan: No mention in George Bush's inauguration speech, though US goal was to "end tyranny in our world"
2 Feb: Mr Bush's State of the Union address says US working with governments in Asia to convince North Korea to abandon nuclear ambitions
There is no sense of panic in the US though there is clearly concern, reports the BBC's Jonathan Beale at the state department.
While Washington insists it is treating North Korea no differently from Iran, there is a clear difference in tone, our correspondent says.
He says that may be in part because North Korea already has a nuclear capability, while Iran probably does not.
The US also believes it still can influence Pyongyang directly if it can resume the talks, while negotiations with Iran are being led by the Europeans.
Several rounds of six-party talks have been held in the past two years but with little progress.
US and other intelligence agencies believe North Korea could already have nuclear weapons, variously estimated at between two and 10.
North Korea's anger appears to be directed at several speeches made by President Bush and other US officials at the start of their new term in office.
"The second-term Bush administration's intention to antagonise the DPRK and isolate and stifle it at any cost has become quite clear," its statement said.
Analysts say Pyongyang 's move may be aimed at trying to gain leverage in the long-running negotiations - hoping to win economic incentives to return to the negotiating table.