He also reiterated the North's call for its own inspection team to be sent to the site of the sinking near the tense Korean sea border.
South rejects proposal
South Korea on Thursday rejected the North's proposal for direct military talks, saying the issue should be handled under the armistice which ended their 1950-53 war.
"The (Seoul) government should focus on discussions at the Security Council," said foreign ministry spokesman Kim Young-Sun.
"It is more appropriate to hold general-level talks between the United Nations Command and North Korea's military and address the issue within the framework of the armistice agreement."
The North has refused to deal with the US-led UN Command based in the South.
In his letter, the North's ambassador also urged the UN council to "take measures'' to help realise these talks before it deals with the results of the international investigation led by South Korea which concluded that North Korea torpedoed the 1,200-tonne Cheonan killing 46 South Korean sailors.
South Korea sent a letter to the council on June 4 asking the UN's most powerful body to respond to the sinking "in a manner appropriate to the gravity of North Korea's military provocation".
Park In-kook, South Korea's UN ambassador urged the council in a letter dated on Wednesday responding to the North Korea proposal "to meet its responsibility to address this issue in an expeditious and credible manner".
The council has been holding consultations since the initial South Korean request but diplomats said China, the North's closest ally and a veto-wielding council member, is opposed to a third round of sanctions against Pyongyang and is also against any direct condemnation of North Korea for the incident.
The diplomats, who spoke on condition of anonymity, said South Korea wants the council to condemn North Korea.
North Korea has warned that its military forces will respond if the council questions or condemns the country over the sinking.
South Korea's Park, also said in the letter, said the ship sinking is a violation of the 1953 Armistice Agreement that ended the 1950-53 Korean War and should be discussed by the UN Command's Military Armistice Commission, which oversees the truce.
He said the commission has twice proposed to North Korea that generals from the North and South meet at the commission to discuss the attack, but the North "has thus far declined to attend these talks".
North Korea has also been internationally criticised by Western powers, prompting the United States to call for Pyongyang to "stop its provocative actions".
PJ Crowley, the US State Department spokesman, said the South Korean-led
international investigation had already assembled evidence that "points clearly to North Korea and a North Korean torpedo".
"We don't think, at this point, that another investigation is warranted. We think the result is clear and compelling.