US President Donald Trump has ramped up his tough rhetoric against North Korea after arriving in Japan, saying that the United States and its allies are prepared to defend freedom and that "no dictator" should underestimate US resolve.

Mr Trump kicked off a 12-day Asian trip and is looking to present a united front with Japan against North Korea through meetings with Prime Minister Shinzo Abe, amid heightened tensions over Pyongyang's nuclear and missile tests.

He told reporters on Air Force One en route to Asia that North Korea would figure prominently in discussions during the trip.

He also singled out trade, which he said had been "badly handled" in the region for years.

Mr Trump has rattled some allies with his vow to "totally destroy" North Korea if it threatens the United States, as well as his dismissal of North Korean leader Kim Jong Un as a "rocket man" on a suicide mission.

A top aide said last week that Mr Trump intends to tell Asian leaders the world is "running out of time" in dealing with the nuclear crisis on the Korean peninsula.

"No dictator, no regime, no nation should ever underestimate American resolve," Mr Trump told hundreds of US and Japanese troops gathered at Yokota AirBase, just west of Tokyo, soon after he arrived.

"Every once in a while, in the past, they underestimated us. It was not pleasant for them, was it?" he said.

North Korea's recent actions, including several missiles that flew over Japan and Pyongyang's sixth and largest nuclear test, have raised the stakes in the most critical international challenge of Mr Trump's presidency.

Recent drills over South Korea by two US strategic bombers have further heightened tensions, and yesterday North Korea released a commentary which ruled out talks and threatened to increase their nuclear arsenal.

"We will never yield, never waver and never falter in defence of our freedom," Mr Trump said.

He told reporters earlier on Air Force One that a decision would be made soon on whether to add reclusive North Korea to a list of state sponsors of terrorism.

Mr Trump said his administration planned to take a different approach after years of what he termed "total weakness."

"We want to get it solved. It's a big problem for our country and the world, and we want to get it solved."

In an apparent attempt to distinguish between North Korea's leadership and ordinary people, he said he thought North Koreans were "great people."

"And I hope it all works out for everybody."

North Korea has warned Mr Trump against making "reckless remarks".

Ruling party newspaper Rodong Sinmun said Americans were pressing for the president's early impeachment because tough remarks by a "spiritually instable" Mr Trump could bring about "nuclear disaster to the US mainland".

Rodong Sinmum cited Bob Corker, chairman of the Senate Foreign Relations Committee, and former officials as saying Mr Trump was pointlessly escalating tensions with the North.

They said the president has not come to his senses and instead is "seriously stimulating the DPRK (North Korea) by making foolish remarks", the paper said in a commentary carried by the KCNA state news agency.

"If the US misjudges the DPRK's toughest will and dares to act recklessly, the latter will be compelled to deal a resolute and merciless punishment upon the former with the mobilisation of all forces," it added.

Japanese Prime Minister Shinzo Abe told reporters before Mr Trump's arrival that he welcomed the visit as a chance to deepen bilateral ties by building upon the "friendship and trust" between the two leaders, fostered by several meetings that included a round of golf in Florida earlier this year.

"I hope we will be able to have thorough discussions about international issues, including North Korea," he said.

Mr Trump also said he planned to meet Russian President Vladimir Putin during his trip, the longest Asian tour by any US leader since George H.W. Bush in 1992.

"I think it's expected that we will meet," he said. "We want Putin's help on North Korea."

Mr Trump wants a united front with the leaders of Japan and South Korea against North Korea before he visits Beijing to make the case to Chinese President Xi Jinping that he should do more to rein in Pyongyang.

Trade will factor heavily during the trip as he tries to persuade Asian allies to agree to policies more favourable to the United States.

A centrepiece of the trip will be a visit to the Asia Pacific Economic Cooperation summit in Danang, Vietnam, where he will deliver a speech in support of a free and open Indo-Pacific region, which is seen as offering a bulwark in response to expansionist Chinese policies.