In a newspaper interview, an individual identified as a representative of the organisation's Army Council said a list of other informers were also being targeted for execution.
The 'Real IRA' representative said the killng of Donaldson had been a "matter of principle" but that it had deliberately delayed claiming the attack.
"We always intended to claim the operation but we wanted to wait until we had first executed crown force personnel. That was secured at Massereene," the representative said, referring to last month's gun assault on the British Army base in south County Antrim.
The interview contains a lurid description of the execution, including the revelation that Donaldson appeared unsurprised by the attack and made little attempt to defend himself.
"The look on his face wasn't even one of shock. He seemed to know what was coming," the spokesman said.
Although he had a long history of involvement in Irish republicanism and was a friend of IRA hunger striker Bobby Sands, Donaldson had come under some suspicion of being an informer for some years before his confession.
As a senior IRA figure and subsequently as a Sinn Féin official, he travelled the world to meet international organisations, providing valuable information for his handlers. In the 1990s, he was sent to run the Noraid office in New York, clashing with its publicity director, Martin Galvin, who came to doubt his motives.
Nevertheless, there was horror among republicans when Donaldson -- a de facto member of the Sinn Féin leadership and the administrator of the party's operation at the Belfast Assembly -- admitted in December 2005 that he had supplied information to British Crown forces for over two decades.
After resigning from Sinn Féin and in the face of an evident threat, he left his Belfast home and lived a hermitic live in a remote, pre-famine Donegal cottage -- until he was uncovered by the 'Real IRA'.
The representative said the seven-strong 'Real IRA' Army Council debated at length whether to kill Donaldson: "Some individuals thought it was better propaganda value keeping him alive because it increased grassroots Provisionals' dissatisfaction with their leadership.
"They were angry at Donaldson's treachery and angry at their leadership for not executing him, for letting him slip off to Donegal unharmed. The Provisional Army Council did a dirty deal with Donaldson like they did with Freddie Scappaticci [another prominent informer].
"But the other argument put forward among our leadership was, that by executing Donaldson, we could show - unlike the Provos - that we weren't prepared to tolerate traitors. We would prove that while the Provos shirked their duty under the green book [IRA rulebook], true and faithful republicans would not."
The group's representative said that a shotgun was used in the execution to reduce the evidence available to any investigation.
It was also revealed there had been no prior interrogation, despite claims that Donaldson might have held valuable information on Britain's network of informers within the (Provisional) Republican Movement.
"There was no need to debrief him because he'd done no damage to our organisation," the representative said.
Other informers, living in Britain or abroad, are also now under threat, it was confirmed.
The spokesman said its prime target is long-serving British agent, Freddie Scappaticci, whose information led directly to the death and imprisonment of scores of republicans.
"Other targets would be [an informer whose alias is Kevin Fulton], Martin McGartland, Christopher Black, Raymond Gilmour and Dave Rupert," he says.
Rupert, an FBI-MI5 agent, was paid millions for successfully infiltrating the Real IRA. His testimony was used to imprison former 'Real IRA' leader, Michael McKevitt.