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"We certainly hope that investigations will shed light on the circumstances of the crash," said Zuma in a statement.
On Saturday night, a helicopter conducting a scheduled aerial patrol of the Kruger National Park – as part of an anti-rhino poaching operation – crashed, killing five SA National Defence Force members on board.
Zuma said the whole country was "saddened" by the loss.
"May their souls rest in peace," said the president.
Brigadier General Xolani Mabanga said that at about 7pm a South African Air Force Agusta A109 light utility helicopter crashed killing five members on board.
"A preliminary investigation is currently underway to establish the sequence of events that led to the fatal crash of the helicopter."
Mabanga said Ministry of Defence and Military Veterans Nosiviwe Mapisa-Nqakula, the chief of the SANDF General Solly Shoke and the chief of the SA Air Force Lt-Gen Zimpande Msimang expressed their heartfelt condolences to the families, loved ones and friends of the deceased.
The death this weekend of the five soldiers closes a difficult week for the country's military, the SA National Defence Union (Sandu) said on Sunday.
"These deaths represent one of the blackest weeks in SA military history," Sandu national secretary Pikkie Greef said in a statement.
Greef said military personnel were putting their own lives in danger in order to help with wildlife conservation.
"SA soldiers are at the forefront of fighting the scourge of rhino poaching in our country."
He said an inquiry must be conducted into the accident.
This week the bodies of thirteen SANDF soldiers killed during a battle with rebels in Bangui in the Central African Republic were brought back home.
Twenty seven other wounded troops are recovering at Pretoria's military hospital. – Sapa