Kim made the remarks while overseeing a joint naval and air force drill simulating an attack on a US carrier strike group off South Korea, the Korean Central News Agency (KCNA) said.
It did not give details of the venue and date of the war games, which were believed to have taken place yesterday.
"He solemnly declared that we have no willingness to sit any longer with the rabid dogs openly barking that they will bring down by the method of bringing about 'changes' the socialist system, the cradle which our people consider dearer than their own lives", KCNA said.
In an interview on YouTube from the White House on January 22, Obama spoke of the eventual collapse of the North Korean regime, calling it "the most isolated, the most sanctioned, the most cut-off nation on Earth".
"We will keep on ratcheting the pressure, but part of what's happening is ... The Internet over time is going to be penetrating this country," Obama said.
"Over time you will see a regime like this collapse," he said, adding the US was looking for ways to accelerate the flow of information into the country".
The North has often used bombastic and sometimes racist rhetoric to slam Obama and other US leaders.
In December its top military body chaired by Kim compared Obama to a "monkey" over his support for the screening of a Hollywood comedy hated by Pyongyang.
"The Interview" -- about a fictional plot to assassinate Kim -- was released online and in theatres despite devastating cyberattacks on its producer Sony Pictures.
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