"While North Korea's nuclear weapon programmemes are a threat not only to our security and that of Northeast Asia, the door to dialogue will remain open so that we can peacefully resolve this threat," Yoon said.
"If North Korea genuinely embarks on a process to complete denuclearisation, we are prepared to work with the international community to present an audacious plan that will vastly strengthen North Korea's economy and improve the quality of life for its people," he added.
Yoon did not elaborate on his plan to re-engage or provide economic incentives to the North. But his national security adviser, Kim Sung-han, told Reuters during the election campaign that the Yoon government would devise a roadmap in early days in which Pyongyang could quickly earn sanctions relief or economic aid in exchange for denuclearisation measures.
Yoon could face a security crisis if North Korea carries out its first nuclear test in five years, as U.S. and South Korean officials warned, after it broke a 2017 moratorium on long-range missile testing in March.
'Troubling speed of anti-intellectualism'
Yoon won the election on a platform of fighting corruption and creating a more level economic playing field amid deepening public frustration with inequality and housing prices, as well as simmering gender and generational rivalry.
South Korea's inflation hit a more than 13-year high last month as Russia's invasion of Ukraine sent commodity prices soaring, boosting expectations of more central bank interest rate rises, which could threaten growth prospects.
Yoon did not mention inflation, but cited low growth, rising unemployment and wage gaps as key economic challenges, pledging to address those by focusing on developing science, technology and innovation.
He blamed anti-intellectualism for polarised politics and deepening internal strife, saying it has threatened to undercut democracy and the people's "sense of community and belonging."
"The political process which has the responsibility to address and resolve these issues has failed due to a crisis in democracy, and one of the main reasons for such failure is the troubling spread of anti-intellectualism," he said.
"When we choose to see only what we want to see and hear only what we want to hear ... this is what shakes our trust in democracy."
Yoon formally assumed his duties at midnight on Monday with a bell-tolling ceremony at Bosingak Pavilion in downtown Seoul.
The inauguration will be held on the front lawn of parliament, attended by some 40,000 people.
Some 300 foreign guests included Chinese vice-president Wang Qishan, Japanese foreign minister Yoshimasa Hayashi, and Douglas Emhoff, the husband of US vice-president Kamala Harris.
The inauguration has been given the slogan "Again, Republic of Korea! A new country of the people" which reflects Yoon's commitment to the people and to resolving regional, class and generational divisions and fostering unity, his team said.
After the inauguration, Yoon moved to a new office at a former defence ministry building inside a sprawling compound.
He has moved the presidential office and residence from the traditional Blue House under a plan, that is estimated will end up costing $40 million, criticised by outgoing president Moon Jae-in as rushed and a national security risk.