South Korean President Lee Myung-bak has described as an "inhumane crime" the North's deadly shelling of a South Korean island last week.
Mr Lee said he felt deep responsibility for failing to protect residents of Yeonpyeong, where two South Korean marines and two civilians were killed.
Pyongyang says it was provoked by Seoul's military drill near the island.
Tension remains high in the area, where the US and South Korea are currently holding joint military exercises.
The aircraft carrier, the USS George Washington, and four other US navy vessels are being joined by South Korean destroyers, patrol vessels, frigates, support ships and anti-submarine aircraft.
The North has described the four-day drill in the Yellow Sea, near the disputed border between the two Koreas, as a provocation.
Firm language
Tuesday's attack was one of the worst clashes between the two Koreas since the end of the Korean War in 1953.
It sparked the resignation of the South's defence minister and angry protests in the South.
In a seven-minute speech to the nation - his first since the attack - Mr Lee pledged that Pyongyang would "pay the price in the event of further provocations".
"Attacking civilians militarily is an inhumane crime that is strictly forbidden in a time of war. I cannot help expressing anger at the North Korean regime's brutality," the president said.
He said the South now realised the North would not on its own abandon its nuclear programme, adding that tolerance would "spawn nothing but more serious provocations".
Mr Lee did not elaborate on how Seoul might respond on any possible aggression by Pyongyang in the future.
The president used very firm language in his speech, the BBC's Chris Hogg in Seoul reports.
But Mr Lee's government has been criticised by opposition lawmakers and by some from his own party who say the military response to the shelling was too soft and too slow, our correspondent says.
Negotiating position
The president's comments come a day after China called for an emergency meeting of key nations to try to defuse the tension.
China has said its "top priority" is to keep the situation under control.
Beijing proposed that members of the six nations that have been taking part in talks on North Korean nuclear disarmament should meet in December.
South Korea's response so far has been non-committal, saying that it will consult other countries.
Mr Lee made no mention of China's call for diplomacy, in what some say was a tacit dismissal of the initiative.
The two Koreas, the US, China, Japan and Russia are involved in the talks.
The six-party talks have been stalled since April 2009. South Korea and the US say they should not resume until the North has made a genuine offer on halting its nuclear programme.
Some analysts say North Korea is trying to raise tensions in order to strengthen its negotiating position and force a resumption of the talks.
It comes as the North is undergoing an apparent transition of power from Kim Jong-il to his youngest son Kim Jong-un.
