President Donald Trump warned on Sunday that “no dictator” should underestimate the United States, as he launched an Asia tour that will be dominated by the North Korea nuclear crisis.

Speaking to cheering military personnel at Yokota Air Base just west of Tokyo, Trump donned a bomber jacket and issued a threat that “no one, no dictator, no regime and no nation should underestimate... American resolve.”

“Every once in a while in the past, they underestimated us. It was not pleasant for them, was it?” roared Trump.

“We will never yield, never waver and never falter in defence of our people, our freedom and our great American flag.”

Trump's marathon trip comes with the North Korea crisis at fever pitch, as US bombers fly sorties over the Korean peninsula and fears mount of another Pyongyang missile test.

According to the Washington Post, Pentagon officials have warned that the only way to locate and secure North Korea's nuclear weapons sites would be via a ground invasion.

N. Korea warns 'instable' Trump against reckless remarks

North Korea on Sunday warned Donald Trump against making “reckless remarks”.

The statement, published in the ruling party newspaper Rodong Sinmun said Americans were pressing for the president's early impeachment because tough remarks by a “spiritually instable” Trump could bring about “nuclear disaster to the US mainland”.

The remark comes soon after Trump's fiery speech during his first stop in Tokyo.

Trump, who will also visit South Korea this week, has been engaged in an escalating war of words with the North's leader Kim Jong-Un, trading threats and personal insults.

In his maiden address to the UN General Assembly he threatened to “totally destroy” the North if it attacked the US or its allies.

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

But 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.

Tensions are high after the North's sixth and most powerful nuclear test in September, along with a series of ballistic missile launches in recent months.

The North says it now has the ability to launch nuclear strikes on the US mainland.

North Koreans 'great people'

The president's first stops are Japan and South Korea ─ frontline US allies in the effort to force Pyongyang to abandon its nuclear programme, and the two countries with most to fear should a full-scale conflict break out.

Trump touched down under clear blue Tokyo skies and stepped out with his wife Melania in bright sunshine to greet the crowds.

Speaking to reporters on the plane, he announced he would likely be meeting Russian President Vladimir Putin during the tour, as the international community scrambles for a solution to the North Korean crisis.

“I think it's expected we'll meet with Putin, yeah. We want Putin's help on North Korea, and we'll be meeting with a lot of different leaders,” said Trump.

He added that North Korea was a “big problem for our country and for the world, and we want to get it solved” but had kind words for the people in the hermit state.

“I think they're great people. They're industrious. They're warm, much warmer than the world really knows or understands. They're great people. And I hope it all works out for everybody,” he said.

The next stop was a golfing date with his “friend” Shinzo Abe, prime minister of Japan, with whom he enjoys a close personal relationship.

Trump joked with reporters on Air Force One that they should not believe him if he claims to outhit Hedeki Matsuyama, one of the world's best players who joined the leaders on the course.

Abe has emerged strengthened from a crushing victory in a snap election and has firmly supported Trump in his policy of exerting maximum pressure on Kim, backed up with the threat of military force.

“I want to further cement the bond of the Japan-US alliance, based on our relations of trust and friendship with President Trump,” Abe said as Trump arrived.

Trump for his part described Japan as a “treasured partner and crucial ally of the US.”

“Trump only has to play golf in Japan, as he knows Japan will follow (the US) whatever happens. Everything has been sorted out beforehand,” Tetsuro Kato, political scientist at Tokyo's Hitotsubashi University, told AFP.

'Appeasement'

After Japan, Trump travels to Seoul, where his relationship with President Moon Jae-in is noticeably cooler.

While Trump has been in regular contact with the hawkish Abe during the North Korean crisis, he pointedly failed to speak to Moon for several days after Pyongyang's second intercontinental ballistic missile test in July.

Trump labelled Moon's dovish approach to North Korea as “appeasement” on Twitter, a comment that did not go down well in the Blue House.

Trump will speak to Korean MPs but not follow the well-trodden path to the Demilitarized Zone dividing the Korean peninsula ─ a visit derided in Washington as a bit of a “cliche.”

From Seoul, Trump travels to China to meet his counterpart Xi Jinping who, like Abe, has solidified his grip on power after being handed a second term.

Trump said before his trip that China could have a “big problem” with “warrior nation” Japan if the North Korea issue is not solved.

He then travels to an Pacific Rim summit in Vietnam before heading to a gathering of Southeast Asian leaders.

Some observers have fretted that a gaffe by the famously ad-lib president could send tensions rising on the peninsula.

“It will be a disaster if he speaks off the cuff and without thinking,” said professor Koo Kab-Woo from the University of North Korean Studies in Seoul.

“If Trump says anything that can provoke North Korea, it could send military tensions soaring again."