US President Donald Trump has said that "talking is not the answer" in dealing with North Korea's military operations.
"The US has been talking to North Korea, and paying them extortion money, for 25 years," he wrote on Twitter.
But the US Defence Secretary, James Mattis, insisted on Wednesday that there was still room for diplomacy.
North Korea has said its firing of a missile over Japan on Tuesday was "the first step" of military operations in the Pacific.
Russian Foreign Minister Sergei Lavrov has told US Secretary of State Rex Tillerson by phone that any further strengthening of sanctions against North Korea would be counter-productive.
Mr Trump's comments come just days after he said that North Korean leader Kim Jong-un was "starting to respect" the US.
On Tuesday, Pyongyang fired a ballistic missile over Japan's northern Hokkaido island, triggering public alerts to take cover before landing in the sea.
Speaking ahead of a meeting at the Pentagon with his South Korean counterpart, Song Young-moo, Mr Mattis said, "We are never out of diplomatic solutions."
Russia has said that US military activity in the region is partly to blame for the increase in tensions, and has urged restraint and called for negotiations.
Mr Lavrov stressed on Wednesday that diplomacy was the only way to overcome tensions on the Korean peninsula, which have been escalating in recent months.
North Korean state media this week also repeated threats to the US Pacific island of Guam, which it called "an advanced base of invasion".
Mr Trump said earlier this month that any such threats would "be met with fire and fury".
The UN Security Council has unanimously condemned North Korea for its military actions.
Meeting late on Tuesday in New York, the council called the launch "outrageous", demanding North Korea cease all missile testing.
While the statement said the regime's actions were a threat to all UN member states, it did not threaten new sanctions against Pyongyang.
North Korea has repeatedly conducted missile launches in recent months, despite being barred from doing so under UN rules.
The latest, a domestically made Hwasong-12, was launched early on Tuesday Korean time from a site near Pyongyang.
It travelled some 2,700km (1,678 miles), at an unusually low height for North Korean missile tests, over Hokkaido before crashing about 1,180km off Japan's eastern coast.
Japan sent out alerts telling people in Hokkaido to take cover. Prime Minister Shinzo Abe later called it "unprecedented, serious and a grave threat".
For the first time, North Korea's official news agency KCNA admitted deliberately firing a ballistic missile across Japan. Previous projectiles which crossed the mainland were later claimed to have been satellite launches.
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
