Fifty-eight sailors were rescued from the choppy Yellow Sea waters off the Koreas' maritime border, but 46 died - the nation's worst military disaster since the 1950-53 Korean war.
Lee urged North Korea to apologise and punish those involved in the alleged attack but Pyongyang has consistently denied involvement in the sinking and has warned that any move to take punitive measures would mean war.
|Lee vowed 'stern measures to hold the North accountable' [EPA]
In a solemn televised address to the nation from South Korea's War Memorial, Lee recounted the "incessant" pattern of attacks by North Korea, including the downing of an airliner in 1987 that killed 115 people.
North Korea, he said, must be punished for its repeated provocations, and Seoul would invoke its right to defend itself if Pyongyang showed aggression again, but he added that "our ultimate goal is not military confrontation".
Lee said the North's commercial ships would no longer be permitted to sail in South Korean waters and that all trade and exchange with the North would be frozen.
Seoul will also take Pyongyang to the UN Security Council over the sinking, he said.
Washington backed Lee's tough rhetoric with strong words of its own on Monday, saying Seoul's sanctions against North Korea were "called for and entirely appropriate".
Barack Obama, the US president, said he "fully supports" Lee's demand that Pyongyang apologise and punish those responsible for the sinking and ordered the US military to work closely with South Korea "to ensure readiness and to deter future aggression", according to the White House.
"...the sinking of the Cheonan ... [is] a very logical result of this collapse in communication and inter-Korea relations"
North Korean specialist
"The Republic of Korea can continue to count on the full support of the United States, as President Obama has made clear," Robert Gibbs, the White House press secretary, said in a written statement.
The US has called for an "international response" to the sinking- without specifying what form this might take – and on Monday the US secretary of state urged China to join that response.
Opening high-level US-China talks in Beijing, Hillary Clinton said North Korea must be held to account for the incident.
China is North Korea's only major political and economic backer, and Beijing has avoided firm public comment on the sinking, instead expressing sympathy for the South Koreans killed and urging all sides to show restraint.
Al Jazeera' China correspondent, Melissa Chan, said China had to perform a juggling act, weighing its relationship with North Korea, against its ties with the US.
The fact that China has been so cautious shows that it is very worried that the situation could lead to all out war, our correspondent said.
'Co-operation has crumbled'
Leonid Petrov, a North Korean specialist and a lecturer in Korean studies at the University of Sydney, told Al Jazeera that relations between the North and South have been deteriorating for some time.
"The inter-Korean relationship is destroyed now, co-operation has crumbled ... the result was the sinking of the Cheonan, and I can see it's a very logical result of this collapse in communication and inter-Korea relations.
"Such accidents could have been easily prevented by diplomatic means - this is something President Lee jeopardised by scrapping the 'sunshine policy' [of rapprochement towards the North]," he said.
The two Koreas are still technically at war because their 1950-53 conflict ended with an armistice, not a peace treaty.