South Sudanese President Salva Kiir Mayardit has called the murder of three children at Rock City in the capital Juba on Saturday a "heinous crime".
The three siblings were identified as Lydia Edward, 9, Blessings Edward, 7, and their 4-year-old sister Nura Edward.
The incident has sparked a public outcry among South Sudanese.
In a statement seen by Radio Tamazuj on Monday, President Kiir offered his condolences to the parents of the murdered children, saying the government will work to "make the criminal pay for his heinous crime".
The South Sudanese leader said he is "shocked and saddened" by the murder of innocent children from one family.
"The pain and trauma inflicted on us by the perpetrator of this crime is enormous, but we, as a country, will prevail. We will work tirelessly to make this criminal pay dearly for this heinous crime y," he stressed.
Kiir directed law enforcement agencies to use every tool in their disposal to quickly apprehend and bring the suspect to justice.
The president described the murder of the three little children as unjustifiable. He appealed to the public to support the investigations by passing information to the police to help them apprehend the suspect.
"As we mourn these children, let us stand in solidarity with their parents and pray that God will give them inner strength to help them cope with this tragedy," he concluded.