The Pentagon said the mission in worldwide airspace showed how seriously President Donald Trump takes North Korea's "reckless behavior".
A White House spokesman said Monday the Trump administration had no reaction to the comments.
The US aircraft, which according to the Pentagon, have reached the closest point to North Korean territory for the first time in recent years, were sent off to North Korea around midnight on Saturday. Trump also used the derisive reference to Kim in his speech to the U.N. General Assembly on September 19.
The latest round of heavy verbal salvoes began when Trump threatened in his maiden U.N. address last Tuesday to "totally destroy" North Korea, a country of 26 million people, if it threatened the United States or its allies.
White House National Security Adviser H.R. McMaster defended Trump's rhetoric and said on Monday he agreed that the risk was that Kim might fail to realize the danger he and his country were facing.
The president said he had personally been against the deployment of U.S. Terminal High Altitude Area Defence (THAAD) system in South Korea, but the decision was made as North Korea's missile capabilities were quickly improving.
However, McMaster also acknowledged the risks of escalation with any US military option. There's not a precision strike that solves the problem.
Meanwhile, China on Tuesday warned that there would be no victor in a potential war on the Korean Peninsula. This has caused heightened security fears on the Korean Peninsula.
Certain North Korean individuals are banned from traveling already due to sanctions imposed because of the country's nuclear weapons program.
We want to hear from you.
She told reporters she held a series of meaningful talks with U.S. Secretary of State Rex Tillerson in NY, and with National Security Adviser H.R. McMaster, Under Secretary of State for Political Affairs Thomas Shannon, Acting Assistant Secretary of State for East Asian and Pacific Affairs Susan Thornton and National Security Council Asia Director Matt Pottinger in Washington.
China's U.N. Ambassador Liu Jieyi said Beijing wanted the situation "to calm down".
He said that pressure on North Korea had increased following a United Nations sanctions resolution.
North Korea's best chance of shooting down a United States plane would likely be with its KN-06 surface-to-air missile system, which its leader Kim Jong-un declared "perfect" in May after previous defects in earlier testing had been addressed. Another possibility is that North Korea is trying to win space to save face as it contemplates whether to de-escalate its standoff with Washington, he said Tuesday.