Iyad Allawi has appointed a member of his bloc to begin coalition talks
The leader of the secular alliance that narrowly won Iraq's parliamentary election has offered to work with all parties to form a coalition government.
Iyad Allawi said his Iraqiya bloc would start by talking with the rival State of Law alliance of Prime Minister Nouri Maliki, which it beat by two seats.
Mr Maliki has refused to accept the result and said he would challenge the count through the courts.
Both the UN and US envoys to Iraq have said the 7 March poll was credible.
There is concern that a challenge to the result could be lengthy and divisive, endangering progress towards greater stability.
Sectarian violence erupted in Iraq as politicians took months to form a government after the last parliamentary election in 2005.
Police on Saturday raised the death toll to at least 52 from twin bombings a day earlier near a restaurant in the town of Khalis, 80km (50 miles) north of Baghdad. More than 70 people were injured in the blasts.
According to final results published by Iraq's Independent High Electoral Commission (IHEC), Mr Allawi's secular Iraqiya bloc won 91 of the Council of Representative's 325 seats, 72 short of a majority.
Mr Maliki's State of Law came second with 89 seats, followed by the Iraqi National Alliance (INA) on 70, and the Kurdistan Alliance with 43.
Iraqiya's narrow victory means Mr Allawi, a Shia, will be given the first opportunity to form a coalition government.
If he fails to do so within 30 days, Iraq's president will ask the leader of another bloc.
On Saturday, the former prime minister said he had already appointed Deputy Prime Minister Rafi al-Issawi, a Sunni member of his alliance, to begin negotiations with other parties in the hope of forming a government "as quickly as possible".
"The Iraqi people have blessed the Iraqiya bloc by choosing it," he told a news conference. "We are open to all powers starting with the State of Law bloc of brother Prime Minister Nouri Maliki."
"Iraq does not belong to anyone or any party, but it belongs to all Iraqis," he added.
Mr Allawi said he was "working for a government that can make decisions and return Iraq back to its place in the Arab and Islamic world".
On Friday, Prime Minister Maliki refused to accept the results, telling a news conference that they remained only "preliminary".
Magdi Abdelhadi, BBC Arab affairs analyst
Iyad Allawi has clearly surprised many with such a forceful comeback. Iraqiya did not win by a big margin, but given the complex and fragmented nature of Iraqi politics, its small victory is still a considerable achievement - if it is not overturned by the courts as his rivals want.
Much will now depend on how he navigates through many of the domestic and regional minefields ahead. The words he spoke struck all the right notes - inclusive and conciliatory towards his enemies both at home and abroad.
Knowing that his comeback will not be welcome in Iran, Mr Allawi must have had them in mind when he said stability in the Middle East was the responsibility of all its peoples, and not just the Americans. The US cannot stay here for ever to protect us, he warned.
If the transfer of power is completed peacefully, and Mr Allawi manages to reconcile the many competing interests, then some will conclude that Iraq's fledgling democracy appears to be coming of age.
He has until Monday to register any complaints with electoral officials.
Mr Maliki is reportedly also negotiating a merger with the INA, which includes followers of the radical Shia cleric Moqtada al-Sadr, so he can claim to lead the biggest bloc in parliament. The groups had been part of the governing United Iraqi Alliance (UIA) before the election, but split acrimoniously.
Iraq's Supreme Court issued an opinion of Thursday specifying that a clause in the constitution referring to the "largest Council of Representatives bloc" could include an alliance formed after an election.
The opinion, published in response to a query submitted by Mr Maliki, might allow State of Law and the INA to claim the right to form a government first. Together, they would hold 159 seats, four short of a majority.
Election officials have refused calls for a recount, and international observers have described the election as fair and credible.
"It is the UN's considered opinion that these elections have been credible and we congratulate the people of Iraq with this success," the top UN official in Iraq, Ad Melkert, told reporters on Friday.
The sentiment was echoed by US Ambassador Christopher Hill and the top US commander, Gen Ray Odierno, who praised the "historic electoral process" and said they backed the conclusions of observers that there had been no evidence of widespread or serious fraud.
A credible election was seen as crucial in helping to stabilise Iraq before the planned withdrawal of US combat troops by the end of August.
Al-Iraqiyya (Iraqi National Movement): Nationalist bloc led by former PM Iyad Allawi, a secular Shia. Includes Vice-President Tariq al-Hashemi, a Sunni Arab, and senior Sunni politician Saleh al-Mutlaq
State of Law: Led by Prime Minister Nouri Maliki and his Shia Islamist Daawa Party, the alliance purportedly cuts across religious and tribal lines. Includes some Sunni tribal leaders, Shia Kurds, Christians and independents
Iraqi National Alliance (INA): Shia-led bloc includes followers of the radical cleric, Muqtada al-Sadr, the Supreme Iraqi Islamic Council (SIIC), and the Fadhilah Party, along with ex-PM Ibrahim Jaafari and Ahmad Chalabi
Kurdistan Alliance: Coalition dominated by the two parties administering Iraq's semi-autonomous Kurdish region - the Kurdistan Democratic Party (KDP) and Patriotic Union of Kurdistan (PUK), led by President Jalal Talabani