On 30 January, voters will elect a 275-member assembly that will appoint a government and draft a constitution.
Speaking on the first official day of campaigning, Mr Allawi vowed to work towards national unity and help those who suffered under Saddam Hussein.
Meanwhile, at least seven people were killed and 30 injured when a bomb exploded in the holy city of Karbala.
The blast, which happened at the gate to a major Shia shrine, the Imam Hussein mausoleum, was the first serious attack in the city following a period of calm.
At least 85 people were killed and 230 wounded in March when co-ordinated explosions near Karbala's main mosque targeted Shias who were celebrating a holy ritual.
Sheikh Abdel Mehdi Karbalai, the local representative of Iraq's most senior Shia cleric, Grand Ayatollah Ali Sistani, was reported to be among the wounded from Wednesday's apparent attack, AFP news agency reported.
Boycott threat
The blast came on the first day of campaigning for elections scheduled for 30 January but it was unclear if there was any political motive.
Electoral authorities say about 80 political blocs have registered to take part in the poll, including Sunni Muslim blocs.
They had threatened to boycott the vote amid fears it could be disrupted by the violent insurgency that continues to rage in Sunni areas.
Mr Allawi announced he would stand at the polls backed by a 240-member list of candidates from his Iraqi National Accord party intended to have a broad appeal.
He said his government would focus on reconciling the country's disparate political strands and rehabilitating former Baathist party members who had not committed crimes.
He pledged to rise above religious and ethnic differences, fight terrorism and develop the rule of law.
Mr Allawi also said he would try to restore the rights of those citizens persecuted under Saddam Hussein's regime and compensate them and their families.
"We strongly reject the injustice and separation of the past and we are working towards national unity," he said.
Candidates busy
BBC correspondent Peter Greste in Baghdad says it is hard to overstate the scale of the mountain that Iraq's democracy still has to climb.
The authorities must set up the physical electoral infrastructure across the country, including in places where the insurgency is still highly active.
More than 230 parties and groups, gathered into about 80 blocs or alliances, have to try to sell their messages amid the violence and chaos.
Correspondents say that, as Wednesday is also the last day for registration, candidates and parties will be busy with administrative issues rather than public campaigning, so no rallies have been planned.
The campaigning begins a day after Mr Allawi announced that leaders in Saddam Hussein's regime would go on trial for crimes against humanity and war crimes as early as next week.
The first to appear would be Ali Hassan al-Majid - better known as "Chemical Ali" - accused of some of the worst crimes committed during Saddam Hussein's decades in power.
Correspondents say the timing of the trials' announcement is being seen as a bid to give Mr Allawi's Iraqi National Accord party a political boost ahead of the polls.
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