Radebe said Justice Ngcobo had informed President Jacob Zuma of his decision, which he said he had taken in order to "protect" the integrity of the Chief Justice and the esteem of the Judiciary as a whole.
There has been uproar since Zuma announced the extension of Ngcobo's term of office, with some questioning the constitutionality of the decision.
"Chief Justice Ngcobo said he found it undesirable for a chief justice to be party in litigation involving the question of whether or not he should continue to hold office, as this distracts from the integrity of the office of the chief justice and the esteem with which it is held," Radebe said.
He went on to say Zuma fully understood and accepted the position taken by the Chief Justice, with the Cabinet Lekgotla underway in Pretoria having been briefed about the matter.
Radebe said: "The President and Cabinet have expressed profound regret at the loss of an outstanding jurist, who has contributed immensely to the country's jurisprudence. The Chief Justice has made a substantial contribution to the judiciary since his appointment by President Mandela in 1996."
Radebe could not say whether Ngcobo would still be eligible to stand when a new Chief Justice is appointed after his term expires on 14 August.