"The DPRK [Democratic People's Republic of Korea] will make consistent efforts for the conclusion of a peace treaty and the denuclearisation through the six-party talks conducted on equal footing," the ministry's spokesman said.
"We take note of the ... statement saying that 'the Security Council encourages the settlement of outstanding issues on the Korean Peninsula by peaceful means to resume direct dialogue and negotiation through appropriate channels'."
'Flip the page'
The disarmament talks involving North and South Korea, the United States, Japan, Russia and China have been in limbo since December 2008.
But China, which had been the host of the six-way talks that began in 2003, on Saturday urged regional powers to "flip the page of the Cheonan incident" and quickly resume the talks.
"We call for an early resumption of the six-party talks and joint efforts to maintain peace and stability on the Korean peninsula," Qin Gang, the foreign ministry spokesman, was quoted as saying by Xinhua news agency.
The US did not immediately respond to the North's offer for new talks.
"At this point we want to let North Korea absorb the fact that the international community has condemned the Cheonan incident," Mark Toner, a US state department spokesman, said.
A South Korean-led international investigation concluded in May that a torpedo fired by a North Korean submarine sank the Cheonan.
But North Korea has called for a new joint investigation by both Koreas and demanded that its inspectors be allowed to visit the site of the sinking near the tense Korean sea border.
Ambassador Sin again pledged that his government will "do our utmost to dig out the truth behind this incident".
The South's defence ministry, meanwhile, said there was no change to its plan to carry out a joint naval exercise with the US in the Yellow Sea, despite objections from China, Pyongyang's main ally.
South Korea's foreign ministry said it welcomed the UN's stance.
"The Security Council's statement is greatly significant as the international community condemned North Korea's attack on the Cheonan with one voice and emphasised the importance of preventing further provocations," it said.
"The government urges the North to respect the spirit of the statement, clearly accept its responsibility and apologise."