"The collusive conduct was never known to, and much less endorsed, by our board," the company's CEO Henry Laas said in an open letter published in the newspaper.
"It was the result of unauthorised actions of a handful of directors in our subsidiary companies," he reportedly said.
Laas said the directors responsible had left the group between 2004 and 2010.
"None of the current executives at Murray & Roberts were found to be at fault."
According to the Sunday Times, Laas said the R309m fine imposed on the company would serve as a "stark reminder of this conduct that must never be repeated".
"I have one fundamental response: an unequivocal apology," he said.
On June 24, the Competition Commission reached a settlement with 15 construction firms, including Murray & Roberts, for collusive tendering in contravention of the Competition Act.
This week, the Cape Times reported that seven major construction and engineering firms met secretly in 2006 to allocate tenders on World Cup stadium projects, and to agree on a 17.5% profit margin.
The newspaper reported that several companies, including Group Five [JSE:GBF], Murray & Roberts, Stefanutti Stocks and Aveng [JSE:AEG], also set up a group called the Western Cape Building Market to share out contracts for three major construction projects in the province.