Coetzee first made revelations about the murder of Kondile to the Harms commission of inquiry in 1990, when he said the activist was shot and burnt near the Mozambique border in 1981.
The policemen implicated in the murder at first denied Coetzee's claims, but have subsequently admitted arranging Kondile's murder and have applied for amnesty.
The TRC's amnesty committee this week heard several versions of the time and circumstances in which Kondile was killed.
Generals Nic van Rensburg and Gerrit Erasmus, Colonel Hermanus Du Plessis, and Sergeant Johannes Raath have all said Kondile was killed on 11 August, 1981 after being released from detention and then adbucted.
They all claim Kondile at first agreed to co-operate with police, but after being given vital information he reneged and remained loyal to the ANC. This necessitated his elimination to prevent the information from reaching the ANC.
Coetzee was recalled to the amnesty committee by Imrann Moosa, appearing for Kondile's mother Charity Kondile, in an effort to ascertain the circumstances of the murder.
Coetzee claims Kondile was killed in late October or early November of 1981 after suffering a head injury while trying to escape interrogation.
He told the committee Van Rensburg asked him to steal an Audi car from a trade union activist and to travel to Jeffreys Bay.
Coetzee said when he arrived at Jeffreys Bay police station Van Rensburg showed him Kondile's car and said the detainee had suffered a head injury after diving through a window while handcuffed.
He said Van Rensburg told him he did not wish to have another "Biko scandal" on his hands.
Coetzee agreed to arrange to have Kondile shot and burnt near the Mozambique border and to abandon Kondile's car nearby to make it appear as if the activist fled into Swaziland.
Coetzee was closely cross-examined by Kobus Booysen, for Van Rensburg and Du Plessis. He was asked about dates and police records. At one stage Booysen put it to Coetzee that he had on many occasions changed records and had not followed correct procedures.
At that point committee chairman Judge Hassen Mall said: "There are many others with similar talents, too."
Coetzee often appeared to have difficulty explaining discrepancies in the various accounts of Kondile's death he had made since his initial revelations. On several occasions he said the errors were "a slip of the mind".
Booyens also put it to Coetzee that he made the revelations about hit squad murders to escape the difficulties he was in at the time.
Coetzee replied that he could easily have taken the easy option by denying claims by his colleague, Almond Nofomela, in a confession about involvement in hit squads hours before going to the gallows for an unrelated murder.
Coetzee said he also had business plans which would have made him millions if he had decided to stay in the country, instead of fleeing to make his hit squad revelations abroad.
Coetzee will continue his testimony under cross-examination on Friday.
A former policeman, Ginotry Danster, who has not applied for amnesty, earlier told the committee he was present when policemen including Du Plessis and Raath tortured Kondile, using suffocation and electric shocks. This has been denied by Du Plessis and Raath.