South Korea has suspended trade with the North and demanded an apology, after a report blamed Pyongyang for sinking a Southern warship.
President Lee Myung-bak said those who carried out the attack, which killed 46 sailors, must be punished.
North Korea's main newspaper called the investigation an "intolerable, grave provocation".
The White House endorsed the South's move, and pledged its co-operation "to deter future aggression".
Meanwhile, US Secretary of State Hillary Clinton has urged China to co-operate with the US on North Korea.
Mrs Clinton told a US-China summit in Beijing that Pyongyang must be held to account for the attack on the Cheonan.
"We ask North Korea to stop its provocative behaviour... and comply with international law," she added.
China is North Korea's closest trading partner and has in the past been reluctant to take tough measures against the communist state.
The North depends on South Korea and China for up to 80% of its external trade and 35% of its GDP. In 2009, inter-Korean trade stood at $1.68bn (£1.11bn) - 13% of the North's GDP.
In a strongly worded televised address, Mr Lee said that the South was forgetting that it shared a border "with one of the most war-mongering nations on Earth".
"From now on, the Republic of Korea will not tolerate any provocative act by the North and will maintain a principle of proactive deterrence," the president said.
"If our territorial waters, airspace or territory are militarily violated, we will immediately exercise our right of self-defence.
"Under these circumstances, any inter-Korean trade or other co-operative activity is meaningless," Mr Lee said, adding that North Korean ships would no longer be allowed to use South Korean water.
And he added: "I solemnly urge North Korean authorities to do the following: Apologise immediately to the Republic of Korea and the international community. Immediately punish those who are responsible for and those who are involved in the incident."
Mr Lee added that South Korea would refer the North to the UN Security Council in response to the sinking of the Cheonan.
But South Korean Unification Minister Hyun In-taek said Seoul would still maintain the joint economic project in Kaesong, even though it would "respond with resolute measures" to possible attempts by the North to undermine the safety of its workers.
The BBC's John Sudworth in Seoul says the measures are probably about as tough a response as the South could take, short of military action.
In his statement of support, US President Barack Obama said: "We endorse President Lee's demand that North Korea immediately apologise and punish those responsible for the attack, and, most importantly, stop its belligerent and threatening behaviour.
"US support for South Korea's defence is unequivocal, and the president has directed his military commanders to co-ordinate closely with their Republic of Korea counterparts to ensure readiness and to deter future aggression," the statement, released by White House spokesman Robert Gibbs said.
South Korea's regional ally, Japan, also said it was considering possible sanctions against North Korea.
The measures came less than a week after experts from the US, the UK, Australia and Sweden said in a report that a torpedo had hit the ship.
They reported that parts of the torpedo retrieved from the sea floor had lettering that matched a North Korean design.
North Korea denies any involvement in the sinking, calling the investigation results a "fabrication" and threatening war if sanctions are imposed.
The South's new measures included resuming psychological warfare against North Korea, which was stopped in 2004, which prompted an angry response from Pyongyang.
"If [South Korea] sets up new tools for psychological warfare such as loudspeakers and leaves slogans for psychological warfare intact, ignoring our demands, we will directly aim and open fire to destroy them," a statement by the military said on Monday.
"More powerful physical strikes will be taken to eradicate the root of provocation if [South Korea] challenges to our fair response," said a commander, according to official news agency KCNA.