In an interview with the BBC, he also refused to say whether an attack on the Pacific US territory of Guam would trigger the military alliance's collective defence clause.
"The reckless behaviour of North Korea is a global threat and requires a global response, and that of course also includes NATO," Stoltenberg told BBC.
"We call on Korea to abandon its nuclear programmes, it's missile programmes, and to refrain from more testing, because this is a blatant violation of several UN security resolutions and it's a threat to international peace and stability," he added.
Asked whether a strike against Guam would be covered under the clause that commits NATO members to come to the defence of each other, he said: "I will not speculate about whether Article Five will be applied in such a situation. What I will say is we are now totally focused on how can we contribute to a peaceful solution of the conflict."