The announcement, carried by KCNA news agency, follows days of strong rhetoric from Pyongyang.
The Pentagon condemned the threats, saying the US was ready to respond to “any contingency”.
South Korea on Tuesday marked the third anniversary of the sinking of the Cheonan ship, in which 46 sailors died.
It said there was no unusual activity in the North.
Tensions remain high on the Korean peninsula in the wake of North Korea’s third nuclear test on 12 February. The test led to new UN sanctions which Pyongyang strongly opposes.
Joint US-South Korea annual military drills have further angered the communist nation. In recent weeks its habitually fiery rhetoric has escalated – it has threatened the US with “pre-emptive nuclear attacks”, as well as strikes on US military bases in Japan.
“From this moment, the Supreme Command of the Korean People’s Army will be putting in combat duty posture No 1 all field artillery units including long-range artillery units and strategic rocket units that will target all enemy objects in US invasionary bases on its mainland, Hawaii and Guam,” the KCNA statement said.
North Korea is not thought to have the technology to strike the US mainland with either a nuclear weapon or a ballistic missile, but it is capable of targeting US military bases in the region with its mid-range missiles.
North Korea’s announcement comes as the country carries out large-scale military exercises, reports the BBC’s Lucy Williamson in Seoul, and it is not clear whether the order applies to the army as a whole or just to specific units.
In response, the US said that it was concerned by any North Korean threats.
“We take everything they say and everything they do very seriously,” Pentagon spokesman George Little said.
“They need to stop threatening peace – that doesn’t help anyone.”
In a press briefing, Chinese Foreign Ministry spokesman Hong Lei said that he hoped that “relevant parties [would] exercise restraint so as to ease the tension”.
The statement came hours after South Korean President Park Geun-hye called on North Korea to “change course” by abandoning nuclear weapons.
Speaking at the national cemetery in Daejeon where the sailors who died when the warship sank are buried, Ms Park said North Korea continued to threaten the South’s national security.
“For the North, the only path to survival lies in stopping provocations and threats, abandoning its nuclear weaponry and missiles, and becoming a responsible member of the international community,” she said.
The Cheonan warship sank in 2010 near the disputed inter-Korean western maritime border. South Korea says a North Korean torpedo sank the ship but Pyongyang denies any involvement.
Months later, North Korea shelled a border island, Yeonpyeong, in the same area, killing four South Koreans, including two civilians. It said it was responding to military exercises in the South.
Meanwhile, websites of associations for North Korean defectors said that their networks crashed earlier on Tuesday. They said that they were victims of a cyber-attack.
Officials said that South Korean broadcaster YTN’s network and a computer network used by seven local governments were also briefly paralysed, Yonhap news agency reported.
Free North Korea Radio, an radio broadcaster, also said that its website “was completely destroyed” after an attack around noon, Yonhap reported.
The presidential office, Cheong Wa Dae, said in a statement that the government was “closely working to confirm if the paralysis cases were caused by technical problems or hacking attacks”.
A cyber-attack on six South Korean banks and broadcasters last week disrupted 32,000 computers and some banking services.
The origin of the attack is not yet known, although there has been speculation that North Korea could have been to blame.
North Korea has been blamed for previous cyber-attacks on the South in 2009 and 2011.