Jackson, who took command of the British army one month before the US-led invasion of Iraq, also said that Rumsfeld was "one of those most responsible for the current situation in Iraq".
In Soldier, his forthcoming autobiography, he accuses Rumsfeld of refusing to deploy enough troops to maintain law and order after the removal of Saddam Hussein, the former president's government.
He also claims that Rumsfeld dismissed detailed plans for the running of post-conflict Iraq that had been drawn up by the US state department.
Sir Mike also said the dossier presented by the government of Tony Blair, the British prime minister, in late 2002 as part of its argument that it was crucial the UK joined the US in the invasion of Iraq, was met with scepticism by both himself and other officers.
'No Iraq threat'
"Its release caused a stir in military circles," he told the newspaper.
He said the suggestion that the UK could face a threat of attack within 45 minutes' notice was particularly dubious.
|Jackson has heavily criticised the way |
Rumsfeld handled Iraq [GALLO/GETTY]
Sir Mike said: "We all knew that it was impossible for Iraq to threaten the UK mainland.
"Saddam's Scud missiles could barely have reached our bases on Cyprus, and certainly no more distant target."
His criticism reveals his depth of anger towards the US administration, and highlights deep-seated tensions between the British command and the Pentagon before and after the invasion of Iraq, the Daily Telegraph reported.
Last month, US officials said that British forces had been defeated in Basra and had surrendered control of the southern Iraqi city to fighters.
However, Jackson defended the British military's activities there.
Jackson told the newspaper: "I don't think that's a fair assessment at all."
"What has happened in the south ... was that primary responsibility for security would be handed to the Iraqis once the Iraqi authorities and the coalition were satisfied that their state of training and development was appropriate.
"In the south we had responsibility for four provinces. Three of these have been handed over in accordance with that strategy. It remains just in Basra for that to happen."
The Daily Telegraph also said that Jackson, who is now retired, believes that the failure of the US-led coalition to defeat fighters was due to the Pentagon's refusal to deploy enough troops.
However, despite his criticism Jackson said he believes the decision to invade Iraq was "legal".
He said he studied the relevant United Nations Security Council resolutions and he concluded that military action was "legitimate under international law without a 'second' resolution" from the organisation.