North Korea told the UN Security Council that the mine explosion was a "sinister obstructive move" by South Korea aimed at portraying Pyongyang's border fortifications as a military invasion.
According to a report by the Korean Central News Agency (KCNA), North Korea's permanent representative to the UN sent the letter to the Security Council president on Sunday.
The letter came amid tensions on the Korean Peninsula after three South Korean soldiers were wounded in a mine explosion on September 21.
Seoul blamed Pyongyang for the incident and called for the restoration of military talks. North Korea rejected the claims and has yet to respond to South Korea's offer to resume communication.
North Korea's letter described the mine explosion as a "sinister obstructive move" by South Korea aimed at portraying Pyongyang's border fortifications as a military invasion.
It also said Seoul is attempting to delay the fortification work and evade responsibility for escalating tensions on the Korean Peninsula.
The letter said the fortification of North Korea's southern border was a "legitimate and just exercise of its sovereignty" in accordance with the UN Charter and international law.
Pyongyang described the work as a defensive measure against external threats of aggression.
"If the RoK violates the sovereignty and territorial integrity of the DPRK despite our warnings, the former will be held wholly accountable for all the ensuing consequences," read the letter.
The Democratic People's Republic of Korea is North Korea's official name, while the Republic of Korea is the official name of South Korea.
The exchange came as South Korea and the US began joint air drills on Monday, a day after Yonhap News reported that North Korean troops were seen conducting drills with a self-propelled howitzer in coastal border areas of Hwanghae province.
The two-week Freedom Flag exercise is being held at Kunsan Air Base in Gunsan, about 180 kilometers (112 miles) southwest of Seoul.
Some 39,000 US military personnel are stationed in South Korea under a mutual defense pact.
The 1950s Korean War ended in an armistice rather than a peace treaty, leaving the two Koreas technically at war.
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