The South African Sunday Times reported that Mr Mbeki had made the announcement to the executive committee of the ruling party, the African National Congress (ANC).
The president has previously insisted that the HIV virus is not the primary cause of Aids - a view which runs contrary to mainstream medical opinion.
More than four million South Africans are infected by HIV, making it one of the worst-affected countries in the world.
The Sunday Times, quoting ANC insiders, reported that Mr Mbeki had told the party's national executive committee that his continued participation in the debate was causing confusion.
The paper said the committee members had mentioned concerns in the government that the controversy sparked by his views was creating a negative mood in South Africa, and causing disillusionment with the president, and widening divisions between the ANC and its Communist Party and trade unionist allies.
Mr Mbeki reportedly told the committee that he would leave it to his ministers - led by Health Minister Manto Tshabalala-Msimang - to liaise with the Presidential Aids Advisory Panel, which Mr Mbeki established this year.
Condemnation
President Mbeki's refusal to accept that HIV is the sole cause of Aids has drawn international condemnation from doctors, scientists and activists - notably at an international conference on Aids and HIV held in the South African city of Durban earlier this year.
More recently, the chairman of the South African Medical Association said it was his organisation's responsibility to end the discussion on whether HIV really causes Aids .
And the leader of South Africa's powerful trade union confederation challenged President Mbeki to acknowledge that the HIV virus is the cause of Aids.
The government refuses to supply the anti-retroviral drugs AZT or Nevirapine to pregnant women to prevent mother-to-child transmission, even though 5,000 HIV-positive babies are born every month.
Tests of Nevirapine are, however, continuing in South Africa.