Little said the United Sates "calls on (North Korea) to refrain from further threats and provocative actions," and said the United States is fully capable of defending itself and its allies, including South Korea and Japan.
New U.N. measures
Tensions are particularly high at the moment because of the new measures against the North adopted unanimously on Thursday by the U.N. Security Council.
"These sanctions will bite, and bite hard," U.S. Ambassador to the United Nations Susan Rice said after the vote.
China, North Korea's key ally, could have used its veto power to block the sanctions. Instead, after weeks of negotiating, it signed on to the final draft.
"China is a country of principle," China's U.N. Ambassador Li Baodong said. "We are firmly committed to safeguarding peace and stability on the Korean peninsula."
On Friday, China's Foreign Ministry called upon "all relative parties to stay calm and refrain from taking actions that may escalate tension." Spokeswoman Hua Chunying reiterated China's support for the sanctions, which have stoked Pyongyang's fury.
The goal of the new sanctions is to stymie the activities of North Korean banks and cash couriers who might be funneling money to the secretive regime's nuclear and missile programs.
It will be tougher for the regime to move large sums of cash stuffed into suitcases, Rice said.
The U.N. resolution also outlines measures to step up scrutiny of suspicious sea shipments and air cargo and it expands restrictions to encompass several institutions and senior officials in the North's weapons industry, as well as a range of materials and technology known to be used in uranium enrichment.
It also blocks the sale of luxury goods, such as yachts and certain high-end jewelry, to North Korea.
"As a result, North Korea's ruling elite, who have been living large while impoverishing their people, will pay a price" for the ongoing nuclear activities, Rice said.
Questions over sanctions' effectiveness
Some doubt whether the new measures will make much difference.
Sanctions imposed after previous nuclear tests and rocket launches have failed to deter Pyongyang.
China will go a long way toward determining whether the new sanctions really do have bite, analysts say.
"As long as China allows North Korea to operate, as long as China provides food, energy assistance and investment, the sanctions really don't matter," said Doug Bandow of the Cato Institute.
North Korea notoriously allows many of its people to live in malnutrition and starvation. Still, the country needs a functioning economy, partly to finance its military, Bandow said.
U.S. State Department spokeswoman Victoria Nuland said the United States is committed to taking action to compel North Korea to alter its approach.
"We're ... going to continue to increase the pressure if they don't make the right choice," Nuland said.