North Korea has been offered compensation if it ends its nuclear weapons programme, on the first day of six-party talks on the crisis.
Talks are focused on the Yongbyon nuclear site
South Korean delegate Lee Soo-hyuck said he outlined a three-step proposal to resolve the stand-off, offering "countermeasures" to reward the North.
Mr Lee said talks began in a "cool and businesslike" atmosphere, as the North and the US outlined opening positions.
Previous efforts to try to end the crisis ended inconclusively in August.
Correspondents say that this time, an agreement to talk again and set up working groups would be seen as progress.
China, US, Russia, Japan, North and South Korea taking part
Set to last until Friday
Parties to sit at hexagonal table, US next to N Korea
In a statement at the start of talks, US envoy James Kelly repeated a call for North Korea to completely, irreversibly and verifiably dismantle its nuclear weapons programmes.
North Korea's chief delegate said his country was prepared to be flexible, but would "stick to the consistent position of our government".
The US and North Korea later held bilateral talks, their first high-level official contact for several months.
North Korea has been demanding economic help and diplomatic recognition in return for a freeze of its plutonium plant at Yongbyon.
But the US has always insisted that North Korea not just freezes, but irrevocably dismantles, its weapons programme before it offers the economic aid and security guarantees North Korea wants.
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Mr Kelly said Washington wanted Pyongyang to end both its plutonium project and an alleged project to enrich uranium.
The BBC's Charles Scanlon in Beijing says this could prove to be the biggest obstacle of all, because North Korea denies the existence of such a programme.
South Korea's proposal to end the impasse is believed to include three phases:
Phase 1: North Korea states its readiness to dismantle its nuclear programmes, in return for which, the US states its readiness to provide security guarantees for North Korea
Phase 2: North Korea dismantles its nuclear programmes. This, once verified, earns North Korea energy aid and other rewards
Phase 3: The resolution of all other issues and the improvement of relations
It was unclear whether the US, or any other party, endorsed the South's offer.
As the meeting opened, the United Nations World Food Programme announced it had resumed food aid to millions of people in North Korea following last-minute emergency contributions.
The WFP issued an urgent appeal for aid earlier this month saying the agency's supplies had nearly run out and that it was cutting off food to almost 6.5 million people.
Supplies have now been partially restored thanks to contributions from Germany, New Zealand, Canada and Norway, the WFP said in a statement. But it warned that more aid was urgently needed in the coming weeks.
The nuclear crisis erupted in October 2002, when the US said North Korea admitted having an enriched uranium programme, in violation of a 1994 agreement.