"They are bluffing that B-1Bs are enough for fighting an all-out nuclear war," CNN cited a statement from KCNA, North Korea's official news agency.
Two of the powerful US bombers, joined by US and South Korean fighter jets, flew over Osan Air Base south of Seoul on Tuesday to show US anger with North Korea's nuclear weapons test on September 9.
Pyongyang claimed Friday's test showed it had a nuclear warhead that could be mounted on ballistic missiles, a possibility that increases fears for US allies in the region and also poses a threat to US bases in South Korea, Japan and Guam.
The US commander in South Korea, Gen. Vincent K. Brooks, called the North's nuclear test "a dangerous escalation" and "an unacceptable threat".
A US intelligence official said North Korea is the only country in the world that threatens others with a nuclear attack, and that Pyongyang shows no signs of backing off its nuclear programme.
North Korea countered on Wednesday saying that it was the US that was inflaming tensions.
"The US imperialists keep letting their nuclear strategic bombers fly over South Korea in a bid to seek an opportunity of mounting a preemptive nuclear attack," the agency statement said.
North Korea's military was prepared to stop any US moves, it said, with a closing warning to Washington.
"They had better stop their rash actions," the statement said.
North Korea on Friday carried out its fifth and most powerful atomic test, in which it reportedly detonated nuclear warheads that can be attached to its missiles.
