Sir John said Tony Blair needed to come up with a strategy to restore stability before coalition troops pulled out.
He also said the government should make a statement on the findings of the Iraq Study Group, headed by ex US Secretary of State James Baker.
And he called for a full inquiry "in due course" into the UK's decision to go to war, so lessons could be learned.
Sir John, who was prime minister during the first Gulf War in 1990, said ministers had so far failed to come up with measures to deal with the Shia militias in Iraq.
'Civil war'
"Unless the Iraqi government can govern and can perform there will be chaos whenever the coalition leaves," he told BBC Radio 4's Today programme.
He added: "If you leave an Iraq in chaos and it develops into civil war that is not just going to be a matter for Iraq, it is going to be a matter for the wider Middle East."
| There was...no intelligence or assessment during my time in the job that Iraq had any intention to launch an attack against its neighbours or the UK or the US Carne Ross |
His words follow claims by a former top diplomat that the government never viewed Saddam Hussein as a threat to the UK.
Carne Ross, who quit his job over the war, said British officials felt the threat from Saddam was "contained".
Mr Ross made his claims in a submission to the 2004 Butler review into Iraq intelligence - it has only just been published because of initial fears it breached the Official Secrets Act.
'No threat'
Mr Ross was head of strategy for the UN mission in Kosovo, and played a leading role in drawing up Britain's policy on Iraq and Afghanistan.
In his Butler evidence, he said that while he worked at the UN, "at no time did HMG (Her Majesty's Government) assess that Iraq's WMD (weapons of mass destruction) posed a threat to the UK or its interests".
Mr Ross added: "We would frequently argue when the US raised the subject, that `regime change' was inadvisable, primarily on the grounds that Iraq would collapse into chaos."
He also claimed that there was no evidence of "significant holdings" of chemical or biological weapons in the possession of Saddam prior to the invasion.
"There was, moreover, no intelligence or assessment during my time in the job that Iraq had any intention to launch an attack against its neighbours or the UK or the US," he added.
Liberal Democrat Leader Menzies Campbell said Mr Blair's justification for going to war had been "systematically destroyed".
He said Mr Ross's evidence was "entirely consistent" with the leaked documents suggesting "the real intention was always regime change."
"If this is true, the British people were knowingly deceived. The prime minister should be ashamed of himself. Parliament and the public deserve an apology."
Mr Blair has always defended the war's legality and the Butler inquiry said there was no evidence of "deliberate distortion" of intelligence on WMD.