Abdullah (R) says Karzai (centre) agrees with his version of the death
On Friday interim leader Hamid Karzai said the killing followed a personal feud with the officials in the intelligence, defence and justice ministries.
But Dr Abdullah told reporters in Kabul on Wednesday: "It was not a premeditated plot."
Mr Rahman's death heightened concerns over the problems of establishing security in Afghanistan after the fall of the Taleban.
Pilgrim mob
The killing of Mr Rahman has been surrounded by confusion and contradictions.
Originally it was reported that an angry mob of pilgrims waiting to fly to Saudi Arabia had killed Mr Rahman, enraged by delays to flights.
That was later flatly denied by Mr Karzai who offered the explanation of a feud.
A number of senior government figures were arrested.
And Mr Karzai has asked Saudi Arabia to extradite suspects who flew out of Kabul after the killing.
Now Dr Abdullah has given credence to much of the original explanation.
"There were three people who entered the plane and pushed Dr Rahman out of the plane," the foreign minister said.
"Then on the ground there were a lot more people involved, including the [pilgrims]."
But Dr Abdullah also there were "high ranking officials in the government" who were under suspicion.
"There might have been people who provoked the [pilgrims]," he said.
And Dr Abdullah insisted the whole government agreed with his account.
Hamid Karzai has not publicly commented on this latest account of Mr Rahman's death.
Government divisions
Earlier on Wednesday a high-level inquiry was launched into the murder.
Two cabinet members - the Labour and Social Affairs Minister, Mir Wais Sadeq, and the Public Works Minister, Abdul Khaliq Fazal - are heading the inquiry team.
Analysts say the appointment of such senior officials to investigate the murder reflects the sensitivity of the case which has laid bare deep divisions within the interim government.
Several of those wanted in the case are senior members of Jamiat-e-Islami, the dominant faction in the Northern Alliance.
Mr Rahman abandoned Jamiat-e-Islami some years ago after an internal dispute.
The Afghan police are also investigating his murder.
But analysts say the police is dominated by members of Jamiat-e-Islami.
They say Mr Karzai's choice of investigators apparently reflects concern that the police might be influenced by their ethnic and political affiliations.