Paul Bremer, the former civilian overseer at the head of the US-led occupying authority in Iraq, dissolved the country's defence ministry and disbanded the armed forces on 23 May 2003.
Those moves, al-Yawir said, contributed to the rise in violence and lawlessness in Iraq.
"Dissolving the ministry of defence and ministry of the interior was a big mistake at that time," al-Yawir told BBC radio on Monday.
"We could have screened people out, instead of screening people in, and this could have saved us a lot of hassle and a lot of problems.
"I firmly believe that the security situation will not be solved unless we have 100% efficient Iraqi forces.
"We have to reinstate some of the clean record of army officers and police officers," al-Yawir added, saying he had made the same argument in Washington last week.
The new Iraqi armed forces and police, launched in August of that year, has since been a target of massive attacks by fighters opposed to the US-backed interim government and US-led forces.
Al-Yawir said the main concern in Iraq was now ensuring people would be able to vote safely. "This is what we are trying to work on right now," he said.