South Korea's new president Park Geun-Hye offered a "more flexible" engagement with North Korea on Friday if Pyongyang chooses a path of trust-building rather than provocation.

In an annual speech marking Korea's 1919 uprising against Japan's colonial rule, Park urged Pyongyang to understand that "nothing will be gained from nuclear development or provocations save for greater isolation and hardship".

Park was inaugurated as South Korea's first woman president on Monday, less than two weeks after North Korea triggered global outrage by conducting its third nuclear test.

"While provocations by the North will be met by stronger counter-responses, the North's willingness to make the right choice and walk the path of change will be answered with more flexible engagement," the president said.

During her election campaign, Park had promised to pursue a trust-building policy with Pyongyang, in contrast to the hardline stance of her predecessor Lee Myung-Bak.

But observers say her immediate options will be limited by the international outcry over the North's nuclear test, which has emboldened the hawks in her ruling conservative party who oppose closer engagement.

Pyongyang has ramped up its bellicose rhetoric in recent weeks, directing dire warnings and threats at both Washington and Seoul as the UN Security Council considers tougher sanctions in response to the test.

Earlier this week, it said South Korea would face "final destruction" if it pushed for a harsh UN resolution, and warned Washington that the US mainland was "well within" the range of its nuclear weapons.

In her speech, Park called on the North to become a "responsible member" of the international community.

"Only then will the path toward shared development by South and North be opened to us and only then will the trust-building process on the Korean Peninsula begin in earnest," she said.

"I urge the North to hasten efforts to normalize inter-Korean relations and open an era of happiness on the Korean Peninsula together with us."

Switching focus to Japan, Park said it was time for Tokyo to assume responsibility for abuses perpetrated during its 1910-45 colonial rule, in order to achieve "genuine" reconciliation between the two neighbors.

"It is incumbent on Japan to have a correct understanding of history and take on an attitude of responsibility in order to partner with us in playing a leading role in East Asia in the 21st century."

While her remarks echoed those made by past South Korean presidents, Park stressed that the historical bitterness between Seoul and Tokyo should not be allowed to fester any longer.

"It is high time for the political leaders of this generation to demonstrate their determination and courage," she said, adding that the "heavy burden of the past" should not be borne by future generations.

"It is necessary for the Japanese government to change unreservedly and behave in a responsible manner," she said.

The two countries are currently navigating the latest flare-up in a bitter and lingering territorial dispute over a small group of islands controlled by South Korea, but also claimed by Japan.