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The aim of the meeting was to understand from both Transnet, responsible for the country's railroads, and Acsa what led to the shortage at Africa's biggest airport, Dipuo's spokesman Bheki Khumalo said on Tuesday.
"The minister will express her concerns about the disruption of jet fuel supply in the country. There's only three days or less of jet fuel and the minister is not happy."
Reserves were usually kept at a five-day level.
Khumalo said Peters wanted the companies to make sure the same thing did not happen during the 2010 Soccer World Cup.
The meeting would take place at the minister's offices in Centurion, Pretoria.
Acsa spokesperson Solomon Makgale said airlines at the continent's busiest airport had been asked to voluntarily cut back fuel use by 30 percent.
About 18 million passengers and 300 000 tons of cargo passed through the Johannesburg airport's terminals annually.
Chief executive officer of the Airlines Association of South Africa Chris Zweigenthal said earlier the shortfall was caused by rail tankers not arriving at an expected rate.
Following a meeting with affected parties on Tuesday, he said the problem had been mostly resolved, with the airport's stockpile likely to return to normal by next week.
Sapa