US Defence Secretary James Mattis has said the US is “never out of diplomatic solutions” in dealing with North Korea.
It comes after President Donald Trump tweeted that “talking is not the answer” to the country’s military ambitions.
Russia has also warned the US against taking military action, saying it would be “fraught with unpredictable consequences”.
North Korea caused alarm by firing a missile over Japan on Tuesday.
The missile, which Japan called an “unprecedented” threat, crossed the northern Hokkaido region early on Tuesday, triggering public alerts to take cover, before landing in the sea about 1,180km (730 miles) off the coast.
North Korea later said it was “the first step” of wider military operations in the Pacific, and repeated its threats to the US Pacific island of Guam.
In a commentary piece, the North’s state news agency KCNA described Japan as a “sworn enemy”, warning that Tokyo’s co-operation with the US was only “accelerating self-destruction”.
Just days ago, Mr Trump had said he believed North Korean leader Kim Jong-un was “starting to respect” the US.
But in a tweet late on Wednesday, he said: “The US has been talking to North Korea, and paying them extortion money, for 25 years. Talking is not the answer!”
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But when asked whether it was true that the US had lost hope in diplomacy, Mr Mattis openly disagreed with the president saying: “No. We are never out of diplomatic solutions.”
He was speaking as he met his South Korean counterpart, Song Young-moo, at the Pentagon.
“We continue to work together, and the minister and I share a responsibility to provide for the protection of our nations, our populations and our interests.”
Russia, which shares a tiny border with North Korea and a maritime border with Japan, has said that US military activity in the region is partly to blame for the increase in tensions.
In a phone call on Wednesday, Foreign Minister Sergei Lavrov told US Secretary of State Rex Tillerson that diplomacy was the only way to overcome tensions on the Korean peninsula, which have been escalating in recent months.
A military solution would be “fraught with unpredictable consequences,” Reuters quoted Mr Lavrov as saying.
He also said any further strengthening of sanctions against North Korea by the UN would be counter-productive.
Meeting on Tuesday, the UN Security Council had unanimously condemned the launch and again demanded North Korea cease all missile testing. But it did not push for new sanctions.
Speaking in Geneva at a UN Conference on Disarmament, North Korean diplomat Ju Yong-chol insisted the North would not be stifled and “will not hesitate to take further tougher counter-measures.”
He said Pyongyang strongly rejected the “fabricated” stories that it was to blame for the tensions of the Korean peninsula.
North Korea’s missile programme:
- North Korea has been working on its missile programme for decades, with weapons based on the Soviet-developed Scud
- It has conducted short- and medium-range tests on many occasions, sometimes to mark domestic events or at times of regional tension
- In recent months the pace of testing has increased; experts say North Korea appears to be making significant advances towards its goal of building a reliable long-range nuclear-capable weapon
- In July, North Korea launched two missiles which it said were Inter-Continental Ballistic Missiles (ICBMs) capable of hitting the US; experts believe they put parts of the US in range
- There is no consensus on how close North Korea is to miniaturising a nuclear warhead to put on a missile