The South African National Defence Force (SANDF) said the plane flew to nearby commercial OR Tambo International Airport in Johannesburg.
The wealthy and politically-connected Gupta family landed wedding guests at the Waterkoof Air Force Base – a national key point – on Tuesday morning.
News of the aircraft landing angered political parties and organisations including the ANC, DA, IFP, Cosatu, and the South African Communist Party.
The Gupta family on Thursday bemoaned what it described as "negative reporting" around the wedding.
"It was planned as a destination wedding to tempt other Indian families to use South Africa as a venue, instead of going to Mauritius or Thailand," the family said in a statement.
"For the record, the family has obtained each and every permission for any and every part of the event." The family said it had not been directly involved in the Waterkloof incident, but had been assured by the Indian High Commission that proper processes were followed and agreements reached with the appropriate officials.
Jet removed
On Thursday, Defence Minister Nosiviwe Mapisa-Nqakula ordered that the jet be removed from the air force base.
The minister further called for an investigation on why the air force was approached with a request to use the base.
She said the international relations and co-operation department agreed to the Indian High Commission's request for the use of it.
On Tuesday, SANDF spokesperson Siphiwe Dlamini said the force was not aware of any permission granted for the Gupta family to use the air force base.
But Gupta family spokesperson Gary Naidoo insisted in a brief statement on that permission was obtained from the SANDF to use the base.
On Thursday, the department of international relations and the South African Revenue Service (Sars) also said they would be investigating how the jet was allowed to land at Waterkloof.
International relations spokesperson Clayson Monyela said neither the department nor the presidency granted executive authority for the aircraft to land at the base.
Monyela said the chief of state protocol, ambassador Bruce Koloane, had been suspended while it conducted its investigation.
Zuma not in attendance
International Relations Minister Maite Nkoana-Mashabane had placed him on compulsory leave with immediate effect. Cabinet said government remained in the dark over who had allowed the private aeroplane to land at the air force base.
Minister in the Presidency Collins Chabane said high-level investigations into the matter were underway.
He also confirmed that President Jacob Zuma, said to be a close ally of the Guptas, was not attending the wedding.
Cosauti in the North West said its members who worked at Sun City complained that the family did not want to be served by the black staff who were employed at the resort.
"They demand that their services must be rendered by white personnel, starting from the cleaning of their rooms, the cooking and the drivers of the shuttles they use in the resort," provincial secretary Solly Phetoe said in a statement.
The Centre of Constitutional Rights of the FW de Klerk Foundation said it was concernedthat public resources were being utilised for the benefit of private associates and that permission must have been given by the respective minister.
"Moreover, bearing in mind the co-ordinated effort, it can probably be assumed that the matter was at least co-ordinated at Cabinet cluster committee level, if not by the presidency itself," the centre's director Johan Kruger said in a statement.
If this was the case heads needed to roll, he said.
Cosatu also complained that the Gupta family was being escorted around by police using state vehicles.
Police Minister Nathi Mthethwa announced on Thursday that national police commissioner Riah Phiyega had launched an internal investigation into the wedding saga.
"I have further instructed that in the event that such transgressions occurred, that the law must take its course on any person found to be responsible," Mthethwa said in a statement.
He said he was expecting a preliminary report by the end of Thursday. – Sapa