The North's official KCNA news agency said Kim Jong Un signed off on the order at a late-night meeting of top generals.
He called the appearance of the two B-2 Spirit bombers an "ultimatum," according to the Australian Broadcasting Corporation (ABC).
"The time has come to settle accounts with the US imperialists in view of the prevailing situation," ABC reported Kim as saying.
Targets include US bases in Hawaii, Guam, South Korea and Japan.
Kim "finally signed the plan on technical preparations of strategic rockets of the KPA [Korean People's Army], ordering them to be stand-by for fire so that they may strike any time," the KCNA report said.
"If they make a reckless provocation with huge strategic forces, the Korean People's Army should mercilessly strike the US mainland, their stronghold, their military bases in the operational theaters in the Pacific, including Hawaii and Guam, and those in South Korea."
The North then advanced its claims with increased military activity, the Yonhap news agency reported.
"North Korea's launch sites to fire off mid- and long-range missiles have recently shown increased movement of vehicles and forces," an anonymous source told Yonhap.
"We are closely watching possibilities of missile launches."
Another official said authorities monitored increased vehicle activity near Tongchang-ri, a west coast missile base in the North.
According to the ABC, North Korea's arsenal includes Soviet-era Scud missiles that can hit South Korea.
Reuters wrote that its longer-range Nodong and Musudan missiles were untested, although they could – in theory – hit US Pacific bases.
The B-2s, meanwhile, were flown from the US and back in what the United States said was a first-time exercise designed to show America's ability to conduct long-range, precision strikes "quickly and at will."
The BBC quoted US Defense Secretary Chuck Hagel as saying Thursday:
"The North Koreans have to understand that what they're doing is very dangerous. We must make clear that these provocations by the North are taken by us very seriously and we'll respond to that."
Pyongyang has been angered by fresh UN sanctions and recent annual US-South Korea military drills.
Analysts in Seoul point out that while North Korea may have the capability of launching missile strikes against South Korea and Japan, Kim Jong-un's call to mobilize them against the continental US represents only bluster.
But in a subtle propaganda ploy, KCNA appears to have purposely included missile attack plans against in the continental US in the background of a photograph of Kim.
Multiple Western businessmen who have worked in North Korea, have told GlobalPost that tensions from the mounting rhetoric and the expansion of UN sanctions this month has made "legitimate" business in the country impossible. It's not clear if that's why the German luxury hotel chain Kempinski halted a project to open a hotel in Pyongyang originally set to open this summer. The company cited only market conditions as a reason.