Sports Minister Fikile Mbalula.
Mbalula, meanwhile, says he will cooperate with public protector Thuli Madonsela's investigation, but insists the claims are baseless.
Madonsela's spokesperson Kgalalelo Masibi told the Star newspaper that Madonsela has assigned an investigator to the case, and the preliminary investigations have begun.
In a written reply to a parliamentary question from the Democratic Alliance, Mbalula said he had taken 240 flights, including 16 international flights, since April 1 2010, costing R1 539 196, according to the report in the Star on Thursday.
In the same period, Oosthuizen had spent R1.1-million on 105 flights, including 29 international flights.
Combined, Mbalula and Oosthuizen racked up 345 domestic and international flights.
That's 186 more flights than Minister of International Relations and Cooperation Maite Nkoana-Mashabane, for whom travel is an essential part of her responsibilities, and her two deputies combined.
Nkoana-Mashabane and her deputies, Marius Fransman and Ebrahim Ebrahim, took a combined 159 domestic and international flights in the same period, said a DA member of Parliament, Winston Rabotapi.
Rabotapi has asked that the chairperson of the committee on sport call on Mbalula and Oosthuizen to explain their travel expenses.
After Thuli Madonsela received a request to investigate the expenditure from DA sports spokesperson Winston Rabotapi in March, the public protector announced in July that the allegations warranted an investigation, leading to the appointment of an investigator who has now begun looking into the matter.
Mbalula's spokesperson Justin Deallende told Eyewitness News on Thursday that the minister would cooperate fully with Madonsela's investigation, while dismissing the allegations as "baseless".
"All the trips and expenses incurred by the minister have been in line with his responsibilities as sport and recreation minister," he said.
Department spokesperson Paena Galane earlier this year tried to explain the number of flights as a necessity for World Cup events.
"Sport, by its nature, is an international event. South Africans participate in international events and we have a duty to give moral support to our athletes when they fly the South African flag," said Galena. – Staff reporter, Sapa