The constitutionality of extraditions was challenged in February by two Botswana citizens, Emmanuel Tsebe and Jerry Phale.
Both Tsebe and Phale were charged with murdering their partners but fled to South Africa.Tsebe has since died.
Before Tsebe's death the pair had applied to the South Gauteng High Court in Johannesburg to prevent their extradition to Botswana, unless their country gave a written assurance that the death penalty would not be imposed. The court granted the order.
Their order was granted, but South Africa's ministers of home affairs and justice and constitutional development appealed to the Constitutional Court, which heard the matter in February.
Lawyers for the ministers argued the High Court had not paid attention to the relevant provisions of the Immigration Act in determining its ruling.
Michael Donen, for the justice ministry, said there were three ways the matter could be dealt with.
The immigrants could either be allowed to walk free, the government could adopt legislation to deal with the matter, or a diplomatic approach could be followed.
Donen said his client had no alternative but to resort to using political clout.
Marumo Moerane, for home affairs, said the Immigration Act provided a systematic way to deal with illegal immigrants, including those with warrants for murder.
He said the government was merely seeking to comply with the Constitution. Though constitutional rights were extended to all people in the country, these two fell into a different category.
"The two [Tsebe and Phale] are prohibited illegal foreigners and liable to be deported."
He said there was no evidence Phale would be convicted for the murder, in which he was implicated by circumstantial evidence. He said if Phale were not deported, he would become a liability to South Africa because he could not find employment.
Anton Katz, counsel for Phale and Tsebe, argued the court order was supported by previous Constitutional Court decisions as well as international law.
Their argument is that under South African law and international law, it is unlawful for South Africa to extradite or deport people to states where they are at risk of being subjected to cruel or inhuman treatment, or the death penalty, in the absence of an assurance that they will not be subjected to this.
The Society for the Abolition of the Death Penalty and a friend of the Court, Amnesty International, support the arguments presented on behalf of Messrs Phale and Tsebe.