North Korea denied responsibility for the Aug. 2 landmine blast in the Demilitarized Zone Monday, urging South Korea to refrain from dampening inter-Korean ties.
The two Koreas reached an agreement last week to ease military tension on the Korean Peninsula and resume the reunion of families separated by the 1950-53 Korean War.
The North expressed regret over the landmine explosion that injured two South Korean soldiers. South Korea said that the North's expression was the equivalent of an apology.
However, the North said that it had nothing to do with the explosion, saying the South is distorting the meaning of the word.
"The South is interpreting the expression of regret to its own advantage," the North's National Defense Committee said in a statement. "At a critical time when the landmark deal should be cherished, South Korea has continued to make comments that could hamper inter-Korean ties."
The Ministry of Unification said the two sides should take follow-up measures sincerely to honor the agreement without blaming each other.
"It's meaningless to quarrel over the wording of the agreement. What is important is to make sincere efforts to implement the agreement," Jeong Joon-hee, ministry spokesman, said.
The statement coincided with President Park Geun-hye's summit with Chinese President Xi Jinping in Beijing.
Some believe the statement showed the North's displeasure with the summit.
"This is a warning message for Park that she should refrain from making any comments on unification or North Korea-related issues that could irritate it," said Yang Moo-jin, a professor at the University of North Korean Studies.
The agreement was reached as the two Koreas appeared on the verge of a military clash following an explosion of North Korean land mines near the inter-Korean border and Seoul's subsequent resumption of its loudspeaker campaign carrying anti-Pyongyang messages.