The "Warriors of the Boer Nation" sent an e-mail to the Afrikaans language "Beeld" newspaper saying it had planted the bombs which killed a woman and injured her husband on 30 October.
The government has previously blamed the attacks on white extremists and, over the weekend, South African police released the names of six men they want to question.
The six men named by the police are believed to be part of another group, Boeremag, or Boer Force, whose leader, Thomas Vogel Vorster, was arrested last month.
The men, Jan Gouws, Gerhardus Visagie, Herman van Rooyen and brothers Kobus, Johan and Wilhelm Pretorius, all face charges of high treason, terrorism and sabotage, said South African police chief Jackie Selebie.
Coat of arms
"We declare that these attacks are the beginning of the end for the African National Congress (ANC) government and accept full responsibility for it," said the message from "Warriors of the Boer Nation".
The letter was also accompanied by the organisation's coat of arms: an upside-down green shield with a sword, flanked by the flags of the old Boer republic and its Afrikaans slogan: "Moenie vrees nie, wees sterk en vol moed" (Don't fear, be strong and have courage), AFP reports.
The group also demanded the release of 35 right-wingers, including Mr Vorster, arrested in connection with a plot to overthrow the government.
Police spokeswoman Sally de Beer told the French news agency, AFP, that they were looking into the claim.
"We are busy investigating the veracity of this letter. We are looking at its origins and are taking it very seriously," she said.
A mosque was also severely damaged and several railway lines between Soweto and Johannesburg destroyed - an act which caused commuter chaos.
South African Defence Minister Mosiuoa Lekota said last week that he suspected the men were former members of the army and police attempting to start a "race war".
"It certainly does not represent the majority of Afrikaners... but a residue within the South African National Defence Force [SANDF] and the South African Police Service," he said.