US President Donald Trump warned Tuesday that Washington was prepared to "solve the problem" of North Korea on its own if necessary as he and Pyongyang engaged in tit-for-tat saber-rattling that sent tensions soaring in East Asia. Trump's warning came as a US naval strike group headed toward the Korean peninsula, a show of force that prompted the nuclear-armed North to declare it was "ready to react to any mode of war desired by the US." "This goes to prove that the US reckless moves for invading the DPRK have reached a serious phase," a spokesman for the North's foreign ministry said, according to state news agency KCNA. The strike group -- which includes the Nimitz-class aircraft supercarrier USS Carl Vinson -- turned toward the Korean peninsula this weekend in response to what a top White House official called a "pattern of provocative behavior." A barrage of recent North Korean missile tests have stoked US fears that Pyongyang may soon have an intercontinental ballistic missile capable of delivering a nuclear warhead to the US mainland. Speculation also has mounted that North Korea might conduct a nuclear test to mark the 105th birthday anniversary of founder Kim Il-Sung on Saturday. US National Security Advisor H.R. McMaster said Sunday that Trump has asked for "a full range of options to remove that threat." White House spokesman Sean Spicer said the presence of a carrier strike group "gives the president options in the region." "I think when you see a carrier group steaming into an area like that, the forward presence of that is clearly... a huge deterrent," he said. - 'Looking for trouble' - In a pair of tweets on Tuesday, Trump doubled down on a vow to act unilaterally against Pyongyang if China fails to rein in its unpredictable ally. "North Korea is looking for trouble," Trump said. "If China decides to help, that would be great. If not, we will solve the problem without them! U.S.A." "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!" Trump wrote in an earlier tweet. The saber-rattling has hit a higher level since a US air strike in Syria last week to punish the regime of President Bashar al-Assad for a suspected sarin attack on civilians. The retaliatory strike, carried out while Trump dined at his Mar-a-Lago estate with Chinese President Xi Jinping, also was clearly intended as a message to Pyongyang. "We will take the toughest counter-action against the provocateurs in order to defend ourselves by powerful force of arms," the North Korea foreign ministry spokesman said. "We will hold the US wholly accountable for the catastrophic consequences to be entailed by its outrageous actions." - Sixth test? - Meanwhile, preparations were underway in Pyongyang for the celebrations marking the birthday of the regime's late founder. Thousands of troops and top military officials gathered in Pyongyang on Monday to pledge loyalty to leader Kim Jong-Un ahead of his grandfather's birth anniversary, state media said. State TV showed thousands of goose-stepping soldiers marching in unison, carrying giant portraits of founder Kim Il-Sung and his son, Kim Jong-Il, in front of the Kumsusan mausoleum where their embalmed bodies are on display. "If they (the US and the South) try to ignite the spark of war, we will wipe out all of the invaders without a trace with... our strong pre-emptive nuclear strike," Hwang Pyong-So, director of the political bureau at the North's army, said in a speech. Kim was not seen at the event televised on Tuesday. The South's prime minister and acting president warned of a "grave provocation" by the North to coincide with other anniversaries, including the army's founding day on April 25. "There is a possibility that the North launches more grave provocations such as another nuclear test to mark a number of anniversaries," Hwang Kyo-Ahn said in a cabinet meeting. Pyongyang has so far staged five nuclear tests, two of them last year, and analysis of satellite imagery suggests it could be preparing for a sixth. Intelligence officials have warned it could be less than two years away from achieving the ability to strike the continental United States. South Korea's top nuclear envoy said Monday after talks with his Chinese counterpart that the two nations had agreed to "strong" new measures to punish Pyongyang if it carried out another nuclear test. The talks came shortly after Trump's summit with Xi. "(We) are prepared to chart our own course if this is something China is just unable to coordinate with us," US Secretary of State Rex Tillerson said after the summit.