The US and North Korea accuse each other of failing to abide by the agreement.
The US and North Korea's neighbours fear Pyongyang's ultimate goal is to put a nuclear warhead on a long-range missile that could target the west coast of the US, but it is not believed to have mastered the technology yet.
BBC: North Korea in nuclear warning after UN rocket resolution
It was the result of a compromise deal between the US and China, North Korea's closest ally.
The talks involving the US, North and South Korea, China, Russia and Japan could get underway again as soon as next month.
The UN resolution, passed on Tuesday, was proposed by the US and backed by China, North Korea's closest ally and biggest trading partner.
The US, South Korea and Japan - who believe North Korea is working to develop long-range missiles capable of carrying nuclear warheads - want action such as the strengthening of sanctions.
Recent reports from South Korean and US bodies which monitor North Korea's nuclear test sites had said North Korea could be preparing for a third test.
The US and other regional allies fear North Korea is working to develop a nuclear warhead small enough to arm a missile, though it is not believed to have achieved this yet.
"They have chosen the path they are on and I am very pleased that we have a unified international community, including China and Russia, in setting forth a very specific condemnation of North Korea and working with us for a firm resolution going forward, " Clinton said, also underscoring the commitments the United States "has and intends to honor" toward South Korea and Japan.
CNN: Clinton slams N. Korea's rhetoric, 'belligerent' actions
Officials from the US, China, North Korea and Japan, among other countries, also sent messages of condolence.
He said he had told officials to increase intelligence-gathering on North Korea, to work closely with the US, China and South Korea, and to prepare for any further unexpected developments.
On Friday, Russia - which shares a border with North Korea - summoned US and South Korean envoys to urge them to cancel the exercises, saying Moscow was "deeply concerned" about rising tensions in the region.
Cai Jian, deputy director of the Centre for Korean Studies at Shanghai's Fudan University, disagrees and tells Global Times that a large-scale military conflict is unlikely to break out because North Korea's threats are largely just psychological warfare against the US and South Korea.
In interviews with China Daily and China National Radio, other Chinese experts strike a more optimistic tone and believe that the US has already softened its stance and is still keeping channels of communication open with North Korea.
For instance, when the US reacted to North Korea's 2006 nuclear and ICBM tests by reinstating the six-party talks in the hopes of appeasing Pyongyang, Iran learned that by exhibiting an interest in engaging the US on its uranium enrichment program it could gain valuable time.
Mr DeTrani added that the US was handling the situation well and that it was up to North Korea to break the cycle.
Six-party talks involving the US, China, Russia, Japan and the two Koreas aimed at ending North Korea's nuclear programme have been stalled since April 2009.
And as Blumenthal notes, the US needs Beijing's help in convincing North Korea to give up its nuclear program.
In one of the most high-profile cases, Mr Clinton negotiated the release in 2009 of two US journalists, Laura Ling and Euna Lee, who had been found guilty of entering North Korea illegally.
The US, Japan and South Korea are seeking a response in the UN Security Council, which banned North Korea from missile tests after nuclear tests in 2006 and 2009.
In a speech, US National Security Advisor Tom Donilon said North Korea should "change course" to obtain the aid and respect it sought.
In public, and for now, it's unlikely that the US will signal any easing of its policy towards North Korea.
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