"The President cannot accede to the demand," said presidency spokesperson Mac Maharaj in a statement.
"President Zuma will not interfere in the work of the Marikana Commission or any other processes, including the prosecution of persons associated with the tragedy."
On Friday, the miners' lawyers, Maluleke, Msimang and Associates reportedly sent a letter to the president, requesting that he release the 270 Marikana miners by 1pm on Sunday.
The City Press reported that if their request was not met, Zuma would face an urgent high court application compelling him to release the miners.
Maharaj said the president would respect the independence of all institutions.
"Including those in the legal sphere, which need to execute their responsibilities without fear, favour or interference," he said.
On August 16, police opened fire on striking workers gathered on a hill near Lonmin's Marikana mine, in North West, killing 34 of them and wounding 78.