SEOUL - North Korea accused the United States on Tuesday of pushing the Korean peninsula to the brink of nuclear war after a pair of strategic US bombers flew over the area in a training drill with the South Korean air force.The two supersonic B-1B Lancer bombers were deployed amid rising tensions over North Korea's dogged pursuit of its nuclear and missile programs in defiance of United Nations sanctions and pressure from the United States.The flight of the two bombers on Monday came as US President Donald Trump said he was open to meeting North Korean leader Kim Jong Un in the appropriate circumstances, even though Pyongyang suggested it would continue with its nuclear tests.South Korean Defence Ministry spokesman Moon Sang-gyun told a briefing in Seoul that Monday's joint drill was conducted to deter provocations by the North and to test readiness against another potential nuclear test.The US air force said in a statement the bombers had flown from Guam to conduct training exercises with the South Korean and Japanese air forces.North Korea said the bombers conducted "a nuclear bomb dropping drill against major objects" in its territory at a time when Trump and "other US warmongers are crying out for making a preemptive nuclear strike" on the North."The reckless military provocation is pushing the situation on the Korean peninsula closer to the brink of nuclear war," the North's official KCNA news agency said on Tuesday.Tensions on the Korean peninsula have been high for weeks, driven by concerns that the North might conduct its sixth nuclear test in defiance of pressure from the United States and Pyongyang's sole major ally, China.Despite that, Trump said he would be "honored" to meet the North's young leader."If it would be appropriate for me to meet with him, I would absolutely, I would be honored to do it," Trump told Bloomberg News in comments that drew criticism in Washington.Trump did not say what conditions would need to be met for any such meeting to occur or when it could happen, but the White House said later North Korea would need to meet many conditions before a meeting could be contemplated."Clearly conditions are not there right now," White House spokesman Sean Spicer said."I don’t see this happening anytime soon."Trump warned in an interview with Reuters on Thursday that a "major, major conflict" with North Korea was possible, while China said last week the situation on the Korean peninsula could escalate or slip out of control.In a show of force, the United States has already sent an aircraft carrier strike group, led by the USS Carl Vinson, to waters off the Korean peninsula to conduct drills with South Korea and Japan.North Korea test-launched a missile on Saturday that appeared to have failed within minutes, its fourth successive failed launch since March. It has conducted two nuclear tests and a series of missile-related activities at an unprecedented pace since the beginning of last year.The North is technically still at war with the South after their 1950-53 conflict ended in a truce, not a treaty, and regularly threatens to destroy the United States, Japan and South Korea.