Still, the United States and South Korea foresee difficulties.
The next round of negotiations is planned for early November. In the interim, informal discussions among the six negotiating nations: the United States, North Korea, China, South Korea, Japan and Russia, are expected.
"We are going to get this done," U.S. negotiator Christopher Hill told The Associated Press in an interview after meetings in Seoul, South Korea. He stressed that North Korea must agree to international restraints before its demand can be considered seriously.
In New York, Secretary of State Condoleezza Rice said "we will not get hung up" on the North Korean demand.
"We can make progress if everybody sticks to what was actually agreed to," Rice said amid meetings with foreign ministers attending the U.N. General Assembly session. "I think we will just stick with the text of the Beijing agreement to which the North Koreans signed on."
CBS News Foreign Affairs Analyst Pamela Falk reports from the U.N. that "with North Korea reneging on a key issue of the new disarmament agreement, U.S. negotiators are trying to keep the six-party talks going because nuclear brinksmanship makes all nations nervous."
"The challenge for U.S. negotiators will be to determine what is a continuing negotiation and what is a stall," added Falk, "and the stakes are high."
Rice discussed North Korea during a meeting later Tuesday with her Chinese counterpart.
"Both agreed that the next round of six-party talks should focus on issues related to the North's dismantlement of its nuclear programs and the verification of that dismantlement," State Department spokesman Sean McCormack said. "They both agreed that the agreement signed in Beijing by the six parties was the binding text for parties, including on the question of light water reactors."
White House spokesman Scott McClellan, meanwhile, said that if North Korea needed some time to reflect on the agreement reached this week, "We'll give it to them."
McClellan told reporters traveling with President Bush to survey Hurricane Katrina relief efforts that the agreement spelled out the steps needed to be taken. "Once they take those steps, then we would be prepared to talk further," he said.