The Seoul Central District Court in February ordered the government to provide some 30 million won ($22,730) in compensation and additional funds for delay to Nguyen Thi Thanh, a survivor of attacks on civilians.
It marked the first legal acknowledgement of South Korea's liability for atrocities during the war.
"We will fully cooperate with the trial proceedings under continued consultations with related agencies to receive an appellate ruling based on substantial truth," the ministry said in a statement to Reuters.
Nguyen, 63, filed a suit against the South Korean government in 2020 seeking about 30 million won in compensation, saying she lost her family members and suffered wounds when South Korean marines killed about 70 civilians in her hometown in Vietnam's central province of Quang Nam in 1968.