North Korean state media warned on Tuesday of a nuclear attack on the United States at any sign of U.S. aggression, as an American navy strike group steamed toward the western Pacific Ocean.

U.S. President Donald Trump, who has urged China to do more to rein in its impoverished neighbour, said in a tweet Tuesday morning that North Korea was "looking for trouble," and the United States would "solve the problem" with or without China's help.

North Korea is looking for trouble. If China decides to help, that would be great. If not, we will solve the problem without them! U.S.A. —@realDonaldTrump

Tension has escalated sharply on the Korean Peninsula, with talk of military action by the United States gaining traction following its strikes last week against Syria and amid concerns the reclusive North may soon conduct a sixth nuclear test.

U.S. Defence Secretary Jim Mattis said the deployment of the strike group — which includes the nuclear-powered flagship aircraft carrier USS Carl Vinson, two destroyers and a cruiser — was not tied to a specific event but a matter of prudence.

"She is just on her way up there because that is where we thought it was most prudent to have her at this time," he said at a Pentagon news conference.

North Korea's official Rodong Sinmun newspaper said the country was prepared to respond to any aggression by the United States.

"Our revolutionary strong army is keenly watching every move by enemy elements with our nuclear sight focused on the U.S. invasionary bases not only in South Korea and the Pacific operation theatre but also in the U.S. mainland," it said.

Early Wednesday, Chinese state media reported that president Xi Jinping discussed the situation in North Korea with Trump in a phone call.

Xi stressed that a resolution of tensions on the Korean peninsula should be achieved by peaceful means, the report said. The phone call came a week after Trump and Xi met face-to-face for the first time at a summit in Florida.

North Korea 'on notice'

White House spokesperson Sean Spicer said Tuesday afternoon that Trump had put North Korea "clearly on notice" he would not tolerate certain actions, but dismissed Pyongyang's nuclear attack threat.

"I think there is no evidence that North Korea has that capability at this time," he said. "Threatening something that you don't have the capability of isn't really a threat."

South Korea's acting President Hwang Kyo-ahn warned of "greater provocations" by North Korea and ordered the military to intensify monitoring and to ensure close communication with the United States.

"It is possible the North may wage greater provocations such as a nuclear test timed with various anniversaries including the Supreme People's Assembly," said Hwang, acting leader since former president Park Geun-hye was removed amid a graft scandal.

Trump said in a tweet that a trade deal between China and the United States would be "far better for them if they solved the North Korea problem."

I explained to the President of China that a trade deal with the U.S. will be far better for them if they solve the North Korean problem! —@realDonaldTrump

Trump and Chinese President Xi Jinping met in Florida last week, where Trump pressed Xi to do more to rein in North Korea.

The North convened a Supreme People's Assembly session on Tuesday, one of its twice-yearly sessions attended by leader Kim Jong-un, and reported a successful national budget execution and personnel appointments, official KCNA news agency said.

There was no mention of its nuclear weapons program or being under threat from the United States, according to KCNA.

South Korean officials took pains to quell talk in social media of an impending security crisis or outbreak of war.

"We'd like to ask for precaution so as not to get blinded by exaggerated assessment about the security situation on the Korean Peninsula," Defence Ministry spokesperson Moon Sang-kyun said.

The North's Foreign Ministry, in a statement carried by KCNA, said the U.S. navy strike group's approach showed Washington's "reckless moves for invading had reached a serious phase."

There was no mention of North Korea's nuclear weapon program or threats from the U.S. during a session of its Supreme People's Assembly, the official KCNA news agency reported. (KCNA/Reuters)

"We never beg for peace, but we will take the toughest counteraction against the provocateurs in order to defend ourselves by powerful force of arms and keep to the road chosen by ourselves," an unidentified ministry spokesperson said.

North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty. The North regularly threatens to destroy the South and its main ally, the United States.

Foreign policy problem

North Korea is emerging as one of the most pressing foreign policy problems facing the Trump administration.

The North has conducted five nuclear tests, two of them last year, and is working to develop nuclear-tipped missiles that can reach the United States.

The Trump administration is reviewing its policy toward North Korea and has said all options are on the table, including military strikes, but U.S. officials said non-military action appeared to be at the top of the list.

Russia's Foreign Ministry, in a statement ahead of a visit by U.S. Secretary of State Rex Tillerson, said it was concerned about many aspects of U.S. foreign policy, particularly on North Korea.

"We are really worried about what Washington has in mind for North Korea after it hinted at the possibility of a unilateral military scenario," the ministry said.

"It's important to understand how that would tally with collective obligations on de-nuclearizing the Korean Peninsula, something that is underpinned in UN Security Council resolutions."

The U.S. navy strike group Carl Vinson was diverted from port calls to Australia and would move toward the western Pacific Ocean near the Korean Peninsula as a show of force, a U.S. official told Reuters over the weekend.

U.S. officials said the strike group would take more than a week to reach waters near the Korean Peninsula.