The premier promised an increase in the strength of Iraq's fledgling security forces, saying they would be better trained and equipped to "defeat the terrorists once and for all".
He said "significant new numbers" would graduate on Thursday and reiterated plans to integrate the paramilitary National Guards into the army.
"Our new tanks and armoured forces will appear for the first time next week to assure stability and security," he said. The security forces took the brunt of Wednesday's violence.
At least 10 policemen were killed when a suicide bomber blew himself up near a police academy in the Shia city of Hilla, south of the capital. There were also 40 policemen among the 44 wounded, an Interior Ministry official said.
"A suicide car bomber blew himself up outside the Babil Sports Club, which is just across the street from the police academy," General Qais Abud told AFP.
Six policemen were also killed in a second suicide bombing when a suicide attacker rammed his vehicle into a police checkpoint in Baquba, north-east of Baghdad, police and medics said. Another 13 people were wounded.
A third bomber targeted a US convoy west of Baghdad, killed one civilian and wounding four.
The al Qaeda-linked army of Ansar Al-Sunna claimed the responsibility for the attack in an Internet statement.
Since late Tuesday, a total of 48 people have been killed in attacks in Iraq as insurgents have made good their threat to try to derail this month's election with a campaign of deadly violence.
The fledgling security forces, which have lost more than 100 personnel since the New Year, are expected to take the lead role in securing polling stations with US-led troops staying in the background and intervening only if called upon.
The prime minister called on all of Iraq's ethnic and religious groups to take part in the election and said he was in talks with groups that had announced boycotts to try to secure a change of heart.
"The Iraqi government and myself personally urge Iraqis to vote and participate in the political process," Allawi said.
"Elections will play a big role in calming the situation and enable the next government to face the upcoming challenges in a decisive manner."
He sought to calm concerns that a boycott by the Sunni Arab former elite would further disenfranchise the community and aggravate the insurgency raging in Sunni areas north and west of the capital.
"For any reason if some would not participate in the elections...it is not the end of the process," he said in English.
"We have checks and balances and other activities that (ensure) ultimately all Iraqis would participate in the political process."
Allawi's British and US backers also voiced determination to press ahead with this month's election.
British Prime Minister Tony Blair said he was committed to elections being held in Iraq as scheduled in order to deny the 'terrorists' a victory.
"I am committed to it, yes, because I think it is extremely important that the terrorists don't gain a victory," Blair told BBC radio.
And the commander of US-led forces in the Baghdad area said that nearly all of the estimated 35,000 soldiers in Task Force Baghdad would be involved in the elections in some way.
"I promise you we will be out in force in support of the Iraqi government, where they want us to be and in consultation with them. We're working those plans right now," Major General Peter Chiarelli said.
The US military said it had arrested more than 60 suspected insurgents and seized significant amounts of weapons and ammunition in sweeps south and west of Baghdad.
Five US soldiers and a marine were killed in attacks on Tuesday.
The deaths brought to 1,336 the number of US military personnel killed in Iraq since March 2003 invasion, based on a Pentagon tally.
In other violence, the bullet-riddled body of a senior member of Iraq's main Sunni faction, the Islamic Party, was found in the street in Mosul seven hours after he was kidnapped by gunmen from his pharmacy in the restive northern city.