The move followed a UN vote last week to expand sanctions on Pyongyang after its February nuclear test.
It comes amid escalating rhetoric from the North over the sanctions and US-South Korean exercises now underway.
On Monday, North Korea cut the hotline between the two Koreas and said the Korean War armistice was "invalid".
Spokesman Jay Carney said the White House was "certainly concerned by North Korea's bellicose rhetoric".
"The threats that they have been making follow a pattern designed to raise tension and intimidate others."
A spokesman for UN Secretary-General Ban Ki-moon, meanwhile, said the terms of the Korean War armistice "do not allow either side unilaterally to free themselves from it''.
The two Koreas remain technically at war because the armistice, not a peace treaty, ended the 1950-53 conflict. Although the hotline has been cut, other channels of communication exist between them.
On Tuesday, a spokesman for South Korean President Park Geun-hye said that her first overseas trip since taking office would be to the US in May, taking into account "the recent Korean Peninsula situation".
North Korea conducted its third nuclear test on 12 February, a move that followed an apparently successful launch in December of a three-stage rocket, seen as a banned test of missile technology.
Regional neighbours and the US fear Pyongyang is working to build a nuclear warhead small enough to put on a missile, but believe it does not yet have the capabilities to do so.'Full range'
Last week, the UN Security Council passed a resolution expanding sanctions on North Korea's financial interests in response to the nuclear test.
North Korea looks set to conduct military exercises in coming days, South Korea saysTo these the US Treasury on Monday added sanctions on the Foreign Trade Bank (FTB) of North Korea and Paek Se-bong, the chairman of the North's Second Economic Committee, which it said oversaw production of ballistic missiles.
The US State Department also added three North Korean officials it said had links to the communist country's proliferation activities.
The sanctions ban any US individual or entity from transactions with those named.
In a speech, US National Security Advisor Tom Donilon said North Korea should "change course" to obtain the aid and respect it sought.
"North Korea's claims may be hyperbolic, but as to the policy of the United States, there should be no doubt: We will draw upon the full range of our capabilities to protect against, and to respond to, the threat posed to us and to our allies by North Korea."
In North Korea, meanwhile, state-run television showed footage on Monday of mass rallies across the country to denounce the US and South Korea, who are currently holding two large-scale annual joint military exercises.
State media also quoted leader Kim Jong-un as threatening to attack a border island, during a visit to a military unit.
He briefed local commanders on turning Baengnyeong Island - which lies close to the disputed inter-Korean maritime border - into a "sea of flames", the KCNA report said.
In March 2010 a South Korean warship, the Cheonan, sank near Baengnyeong Island with the loss of 46 lives. South Korea said a North Korean torpedo strike was to blame; North Korea denied any role in the incident.
