(CNN) -- South Korea's president said Monday the country should respond to the attack on Yeonpyeong Island the same way the United States reacted to the September 11, 2001, attacks in New York -- by using the event as an opportunity to reflect on security and overhaul the country's defenses.
Speaking during his New Year's address, President Lee Myung-bak called the November attack a turning point and warned North Korea that any future "provocations" would be met with "stern, strong responses."
"The shelling of Yeonpyeong Island ... served as an opportunity for us to reflect on our security readiness and overhaul our defense posture," he said. "Peace cannot be obtained without a price."
Tensions have been running high between North and South Korea ever since the sinking of the South Korean warship Cheonan last March, killing 46 sailors.
South Korea and the international community blamed the North for the sinking, but Pyongyang has denied the accusations.
Last month, North Korea said the South's navy fired into Northern waters and, in retaliation, it shelled Yeonpyeong Island, killing four South Koreans.
"We cannot let North Korea covet even an inch of our territory. Any provocation that would pose a threat to our lives and property will not be tolerated," said Lee.
Over the weekend, officials in North Korea called for better ties with South Korea, according to South Korea's Yonhap News Agency. North Korea urged dialogue and cooperation in 2011 and asked the South to end its military exercises.
South Korea's president said in his televised address that North Korea needs to work toward peace with deeds as well as with words.
"I remind the North that the path toward peace is yet open. The door for dialogue is still open. If the North exhibits sincerity, we have both the will and the plan to drastically enhance economic cooperation together with the international community," he said.
The U.S. special envoy for North Korea, Stephen Bosworth, is expected to travel to South Korea, China and Japan this week to discuss next steps on the Korean Peninsula. His first stop is Seoul.