SEOUL, South Korea — South Korea’s president on Monday opened the door to possible peace talks with North Korea even as he vowed not to let Pyongyang "covet even an inch of our territory" — looking to strike a delicate balance between diplomacy and strength two days after the North called for better ties with Seoul.

Lee Myung-bak, addressing the country in a New Year’s speech, said the Nov. 23 shelling of Yeonpyeong Island, which killed four and has spiked fears of war, should be treated as the United States did the Sept. 11, 2001, terrorist attacks and spur the South to change the way it defends itself. Future provocations, he said, "will be met with stern, strong responses."

However, he said: "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."

On New Year’s Day, the North called for warmer ties and the resumption of joint projects with South Korea. Pyongyang, eager for food and fuel assistance, has said it wants stalled international aid-for-nuclear-disarmament talks to restart. Washington and Seoul have said no, demanding the North first fulfill past nuclear disarmament commitments.

Meanwhile, the United States, which has about 28,500 troops in the South, is sending its top envoy on North Korea, Stephen Bosworth, to Seoul for talks Wednesday with top officials. U.S. Defense Secretary Robert Gates will visit Seoul next week.

North Korea on Monday called for Seoul to scrap its hostile policy against Pyongyang.

"As long as South Korea’s dangerous northward invasion plot is maintained, North-South Korea relations cannot be improved at all and we cannot think about the nation’s safety and peaceful reunification," the North’s main Rodong Sinmun newspaper said in a commentary carried by the official Korean Central News Agency.

In the North Korean capital, about 100,000 people gathered Monday for an annual New Year rally to display loyalty to leader Kim Jong Il.

The crowd packed Kim Il Sung plaza, pumping their fists in the air and shouting slogans while carrying huge portraits of Kim and his father, North Korean founder Kim Il Sung. Some waved huge red flags and played small drums, as top officials watched from an elevated viewing stand. Kim and his son and heir-apparent, Kim Jong Un, didn’t appear in the footage broadcast by APTN.

Despite the mention of possible peace talks, the focus of Lee’s comments on North Korea was a tough promise to improve South Korea’s defenses.

Lee was severely criticized for acting too slowly and too weakly after the shelling near the Koreas’ disputed western sea border. It was the first attack by the North, which claims the waters around the island as its territory, on a civilian area since the 1950-53 Korean War. Lee’s government has responded by replacing the defense chief, strengthening security and pushing to deploy additional troops and weaponry to Yeonpyeong, which lies just seven miles (11 kilometers) from North Korean shores.

After the Sept. 11 terrorist attacks, Lee said, the United States devised new security strategies. "The shelling of Yeonpyeong Island also served as an opportunity for us to reflect on our security readiness and overhaul our defense posture," he said.

Under Lee’s conservative administration, relations between the two Koreas have deteriorated as he reversed policies of earlier liberal-leaning administrations that he saw as rewarding the North’s aggression.

Presidential and foreign ministry officials said the resumption of talks with North Korea would depend on whether Pyongyang makes progress on past nuclear commitments.

Jeung Young-tae, an analyst with the government-funded Korea Institute for National Unification in Seoul, said tensions won’t be dramatically eased anytime soon because North Korea won’t accept linking new talks with disarmament efforts.