Pyongyang regularly issues belligerent warnings of war if provoked by the South or the U.S.
On Monday, the powerful National Defense Commission criticized Lee's speech as a "clumsy farce," according to the official Korean Central News Agency.
"This is an open breach of the inter-Korean military agreement, a grave military provocation and a serious incident driving the inter-Korean relations to the worst phase," a news anchor said on North Korean state TV.
One 23-year-old university student in Seoul said she feared war.
"I'm genuinely scared that this will escalate into a full-on war," Do Yoon-hee said as she watched a replay of the president's address on her cell phone. "I don't feel that these countermeasures keep us safer."
Businessman Park Joo-shin, however, doubted fighting would break out again on the Korean peninsula.
"An all-out war would be suicidal for Pyongyang," he said.
The truce prohibits South Korea from waging a unilateral military attack, so Seoul sought Friday to strike at Pyongyang's faltering economy.
Seoul carried out $1.68 billion in trade with North Korea in 2009, about 33 percent of Pyongyang's total trade, according to the Korea Trade-Investment Promotion Agency. China is North Korea's biggest trading partner, with commerce totaling $2.68 billion last year — about 53 percent of the North's total, KOTRA said.
Imports of sand and other goods will be halted, and North Korean cargo ships will be denied permission to pass through South Korean waters, Unification Minister Hyun In-taek said.
The biggest source of trade — a joint factory park in the North Korean border town of Kaesong where some 110 South Korean firms employ about 42,000 North Koreans — will remain open, Hyun said.
The suspension of imports will deal a "direct blow" to North Korea, the state-run Korea Development Institute said.
Lim predicted, however, that the North would make up the loss by finding Chinese partners.