North Korea says war is now inevitable between Washington and Pyongyang.
"Series of violent war remarks coming from the USA high-level politicians amid such circumstances have made an outbreak of war on the Korean peninsula an established fact", the spokesperson said.
Nauert said North Korea was "not showing any interest in sitting down and having any kind of serious conversations when they continue to fire off ballistic missiles".
"Through the exercise, the South Korean and US air forces have demonstrated the alliance's strong will and capability for strong retaliation against North Korea's nuclear and missile threats", the Joint Chiefs of Staff said in a statement.
US Republican Senator Lindsey Graham urged the Pentagon on Sunday to start moving US military dependants out of South Korea, saying conflict with North Korea was getting close.
North Korea launched its new Hwasong-15 missile a week ago, claiming to have achieved its goal of becoming a nuclear state. "When we overcome this ongoing crisis, I am sure it will turn into an opportunity to dramatically improve the South-North relations", he added. The foreign minister referenced a comment by the United States envoy to the UN, Nikki Haley, in which she said that North Korea would be "utterly destroyed in case of war", calling it a "bloodthirsty tirade".
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"B-1B bombers have been regularly dispatched to the Korean peninsula over the past years; however, it seems that the US Air Force might have enhanced its training to better prepare for actual warfare", he said.
While B-1Bs are no longer equipped to carry nuclear weapons of their own, they would be key to any strike targeting major North Korean facilities, he said.
The number of jets in the air between the US and South Korea is 230.
As tensions soar, such drills are increasingly provocative, but also increasingly risky, with the ever-present threat that North Korea will interpret a drill as a real attack and retaliate, starting a full-scale war.
The US-South Korea drills coincide with a rare visit to the North by United Nations political affairs chief Jeffrey Feltman.
Russian Federation and China remain behind a so-called "double-freeze" proposal, which would see the USA suspend joint drills with South Korea in exchange for Pyongyang halting its missile and nuclear tests. Some analysts and diplomats hope his visit could spark a UN-led effort to defuse tensions.