His rival, Muqtada al-Sadr, who fought against the American occupation in 2004, is the clear victor in most southern parts of the country as well as in Baghdad, which has the most allocated seats.
U.S. Defense Secretary Jim Mattis said Tuesday that the United States stands by Iraqis' electoral choices, despite the surprise success of populist Shiite cleric Moqtada al-Sadr, who fought U.S. troops during the Iraq War.
Meanwhile, allegations of vote rigging in northern Iraq were delaying final results on Tuesday, with some Kurdish parties demanding a re-run of the weekend's poll.
Responding to Mr Abadi's comments, Mr Al Sadr described his victory as "an achievement for the Iraqi people and its national entitlement". Mr. Sadr, who once called for attacks on American forces, capitalized on this widespread discontent by rebranding himself in recent years as a champion of the poor, a firebrand against corruption and a patriot who rails against outside interference by Iran as well as America.
Some prominent politicians now believe that al-Abadi is still the favorite to form the next government despite losing.
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"Given the unexpected results that Nasr achieved, the chance of Abadi becoming the [next] prime minister has decreased, especially since the [coalition] under his leadership came in fifth in Baghdad", argued Tasnim. The group overran a third of Iraq in 2014. In fact, this complicated reality could lead to weeks if not months of negotiation to form the next government.
Although Saturday's election was largely peaceful, less than half of the country's 24.5 million voters headed to polling stations - the lowest turnout since the country's first multiparty elections in 2005. Full results are due to be officially announced later on Monday.
The Reformist Shargh newspaper wrote that the surprising results of the Iraqi elections may signal a greater Saudi influence in Baghdad.
"I can just say the independent high electoral commission - that's basically the Iraqi equivalent of the federal election commission - they are investigating".
Reuters calculations based on the document showed Sadr had won the nationwide popular vote with over 1.3 million votes and gained around 54 of parliament's 329 seats.