The North Korean military issued a fresh burst of ominous rhetoric Thursday, warning that U.S. bases in Guam and Japan are within its "striking range."

The statement from the Supreme Command of the Korean People's Army, carried by the North's state-run news agency, follows the announcement by the United States this week that its B-52 bombers were making flights over South Korea as part of annual military exercises.

"The U.S. should not forget that the Andersen Air Force Base on Guam where the B-52s take off and naval bases in Japan proper and Okinawa where nuclear-powered submarines are launched are within the striking range of the DPRK's precision strike means," the North Korean military said Thursday.

Despite Pyongyang's rhetoric, no U.S. Navy submarines are based in Okinawa or anywhere else in Japan, although they may make calls at U.S. bases there. DPRK is short for Democratic People's Republic of Korea, North Korea's official name.

Citing what it called the United States' "nuclear blackmail and threat," the North said it that it, too, would "take corresponding military actions."

Pyongyang had already reacted angrily to the B-52 flights, warning Wednesday of "strong military counteraction" if the planes made more sorties over the Korean Peninsula.

Angry words after new sanctions

Tensions have spiked in the region since North Korea carried out its latest underground nuclear test last month, the first under its new young leader Kim Jong Un, prompting the United Nations Security Council to respond by toughening sanctions on the secretive regime.

The sanctions enraged the North further, and during the week when the Security Council was voting on them, it ratcheted up its threats, suggesting it could carry out a pre-emptive nuclear strike on the United States and South Korea.

Although analysts and American officials say Pyongyang is still a long way from being able to carry out such an attack on the U.S. mainland, the United States' bases in Japan and Guam appear to be within range of the North's conventional weapons.