The announcement follows a fresh round of UN sanctions punishing Pyongyang for its nuclear test last month.
Earlier, Pyongyang said it reserved the right to a pre-emptive nuclear strike against its "aggressors".
The US said it took the threats seriously, but that "extreme rhetoric" was not unusual for Pyongyang.
South Korea's defence ministry said that the North would become "extinct" if it went through with its threat.
The North Korean announcement, carried on the KCNA state news agency, said the North was cancelling all non-aggression pacts with the South and closing the main Panmunjom border crossing inside the Demilitarized Zone.
The threatened pre-emptive nuclear strike seems more bluff than reality, since the North's leaders know it would be suicidal, and an attack on the US seems impracticable given the still technically rudimentary quality of the North's ballistic missile programme and the unproven state of its nuclear miniaturisation technology needed to place a nuclear warhead atop a missile.
A more troubling possibility is that the North might choose - out of irritation with the UN - to precipitate a border clash with South Korea, either on land or sea, as it did before in 2010.
It also said it was notifying the South that it was "immediately" cutting off the North-South hotline.
The hotline, installed in 1971, is intended as a means of direct communication at a time of high tension, but is also used to co-ordinate the passage of people and goods through the heavily fortified Demilitarized Zone.
KCNA said the hotline, which has been severed several times before, "can no longer perform its mission due to the prevailing grave situation".
North Korean leader Kim Jong-un is also reported to have visited front-line military units that were involved in the shelling of a South Korean island in 2010.
KCNA said he had urged the soldiers there to keep themselves ready to "annihilate the enemy" at any time, and reconfirmed so-called "enemy targets" on five islands in the West Sea.'Extreme rhetoric'
Seoul's defence ministry spokesman Kim Min-seok said that if the North were to carry out a nuclear attack on South Korea it would become "extinct from the Earth by the will of mankind".
North Korean TV has been showing images of Kim Jong-un visiting troops at undisclosed locationsHe also warned that in response to any provocation from the North, Seoul would "immediately" turn the US-South Korean military drills currently being conducted "into a punishment mode to respond to it as planned".
The US, the main focus of North Korean ire, said it was capable of protecting itself and its allies from any attacks.
"One has to take what any government says seriously," State Department spokeswoman Victoria Nuland said of the nuclear threat.
"It is for that reason that I repeat here that we are fully capable of defending the United States. But I would also say that this kind of extreme rhetoric has not been unusual for this regime, unfortunately."
Senator Robert Menendez, who chairs the Senate Foreign Relations Committee, said North Korea knew what the cost of any attack would be.
Strongly condemns North Korea's ongoing nuclear activities, including its uranium enrichment programme
Imposes new sanctions to block financial transactions and bulk cash transfers in support of illicit activity
Strengthens states' authority to inspect suspicious cargo
Requires states to deny port access to any North Korean vessel that refuses to be inspected
Calls on states to deny permission to any aircraft to take off, land in or overfly their territory if the aircraft is suspected of transporting prohibited items
Enables stronger enforcement of existing sanctions by UN member states
Sanctions new individuals and entities
"I don't think that the regime in Pyongyang wants to commit suicide, but that as they must surely know, that would be the result of any attack on the United States," he said.
On Thursday, the UN Security Council in New York unanimously backed Resolution 2094, imposing the fourth set of sanctions against the North.
The resolution targets North Korean diplomats, cash transfers and access to luxury goods.
It imposes asset freezes and travel bans on three individuals and two firms linked to North Korea's military.
South Korea's ambassador to the UN, Kim Sook, said it was time for North Korea to "wake up from its delusion" of becoming a nuclear state.
"It can either take the right path toward a bright future and prosperity, or it can take a bad road toward further and deeper isolation and eventual self-destruction," he said.
US ambassador to the UN Susan Rice said the sanctions would "further constrain" North Korea's ability to develop its nuclear programme.
She warned that the UN would "take further significant actions" if Pyongyang were to carry out another nuclear test.
Chinese Foreign Ministry spokesman Qin Gang issued a statement supporting the UN resolution and describing it as a "moderate response".
He said China - North Korea's sole ally - urged "relevant parties" to stay calm and said the main priority was to "defuse the tensions, bring down heat" and restart negotiations with Pyongyang.
Before the UN vote, Pyongyang accused the US of pushing to start a war.
"As long as the United States is willing to spark nuclear war, our forces will exercise their right to a pre-emptive nuclear strike," said North Korea's foreign ministry, in a statement carried by the KCNA news agency.
