North Korea has set out the concessions it wants in order to scrap its nuclear weapons programme.
The six nations have not sat down together for 13 months
On the second day of six-party talks in Beijing, North Korean officials said they wanted the US to remove its own nuclear arsenal from South Korea.
They also reportedly called for renewed diplomatic relations with Washington.
Washington said more than a decade ago that it no longer had nuclear arms in the Korean peninsula.
The US has already made clear it is not prepared to discuss mutual disarmament with North Korea.
Instead it has said it will offer security guarantees and economic assistance in return for a complete end to Pyongyang's nuclear programme.
All the six nations involved in the nuclear talks are thought to have presented their basic positions at Wednesday's session. As well as the US and North Korea, delegates from Japan, China, Russia and South Korea were also around the table.
Oct 2002: US says North Korea is enriching uranium in violation of agreements
Dec 2002: North Korea removes UN seals from Yongbyon nuclear reactor, expels inspectors
Feb 2003: IAEA refers North Korea to UN Security Council
Aug 2003: First round of six-nation talks begins in Beijing
Feb 2005: Pyongyang says it has built nuclear weapons for self-defence
Wu Dawei, China's chief delegate at the talks, told Beijing media that the six countries involved should "seize the opportunity to resolve the challenges, and jointly chart a better future for North East Asia".
This fourth round of six-party talks marks the end of a 13-month boycott by North Korea.
Unusually for these discussions, no end date has been set, in what analysts say is a sign that the delegates are determined to move forward and make progress.
But a BBC correspondent monitoring the talks in Beijing, Charles Scanlon, says there is little expectation of a breakthrough.
The North has been demanding equal treatment as a nuclear power since claiming in February that it had built atomic bombs.
Its offer on Wednesday to scrap its nuclear programme if the US also removes nuclear weapons from the Korean peninsula is unlikely to lead to much progress: The US has already denied having nuclear arms in the region.
South Korea's Yonhap news agency said the North had also called for diplomatic relations with Washington, a formal peace mechanism, and an end to what it called the Bush administration's "hostile policy".
For its part, the US brought up North Korea's ballistic missile programme and its poor human rights record, reports said.
Before the talks, Washington made it very clear that it would not discuss any kind of pact with North Korea until the nuclear issue was resolved.
The US has even indicated that the country could face further sanctions if no solution is found.
But according to our correspondent, despite the deep differences that remain between the delegates, some participants say the mood remains positive.