Abadi is banking on his achievements in office to win a second term at May 12 elections
Abadi even went on a rare tour of Kurdish provinces last month although few rate his chances highly of recruiting Kurds.
Many of Iraq's Sunni Arabs also feel lingering resentment towards the Shi'ite-led government following the war and devastation that mostly hit their areas with the advent of Daesh.
So while many prefer Abadi to other Shi'ite politicians because he has signalled a move away from sectarianism, that may not necessarily translate into votes for his candidates.
Abadi also faces criticism about persistent corruption, tough economic conditions exacerbated by fighting and the austerity measures his cabinet introduced, as well as his pro-business stance in a country where most people are state employees and distrust the private sector.
"Abadi is a cultured man and a conciliatory politician, but he also brought us austerity," said Mohamed Ghadban, a student in the Shi'ite holy city of Najaf.
Mindful of this weakness, the prime minister's campaign narrative has also focused on the defeat of Daesh.
Abadi declared victory in December after a brutal three-year campaign to free Iraq from the militants who at one point controlled a third of the country.
To do so, he oversaw simultaneous and conflicting support from the United States and Iran, each awkwardly sidestepping the other in the widening regional conflict to defeat Daesh.
As the U.S.-led coalition focused on rebuilding and training the depleted Iraqi security forces while launching near-daily air strikes, Iran-backed Shi'ite militias were embedding deeper into the fabric of Iraq's society and state apparatus while providing vital military support to government forces.
Abadi's deft juggling of Iran and the United States amid escalating tensions over the Iran nuclear deal, has made him the preferred candidate for Western allies, who have little to show since invading Iraq 15 years ago beyond violence, endemic corruption and defective state institutions.
Abadi has also gained praise for courting Iraq's Sunni Arab neighbours, a strategy diametrically opposed by Maliki.
Though Abadi's supporters and foes agree he is not a natural politician, they say he has grown in confidence since his nervous start four years ago. However, he is seen as an indecisive leader, preferring to deliberate at length with advisers and lawmakers.
Three Western diplomats in Baghdad said their governments would find Abadi the easiest candidate to work with but that very pliability is seen as a weakness by some constituents who consider him a foreign stooge.
"Abadi is a decent man, but he's not in control of his own choices," said Falah Abdullah, a 65-year-old retired police officer in Qayyarah, 60 km (40 miles) south of Mosul. "He alternates between what Iran wants and what America wants."
This has much to do with his predecessor's legacy. A polarising figure, Maliki's spectre looms large in the 2018 election, particularly given the split in the Shi'ite vote.
Despite many blaming him for losing swathes of territory to Daesh and institutionalising corruption in Iraq's bloated ministries, Maliki is still seen by his considerable base of supporters as a strong leader who stood up to the West and defends Shi'ite interests.
Abadi also faces stiff competition from Amiri, the leader of the Badr Organisation, Iraq's biggest Iranian-backed Shi'ite militia, who is also campaigning on a victory narrative.
Amiri was commander of the Popular Mobilisation Forces, a coalition of Iranian-backed militias that played a large role in defeating Daesh after a call to arms by Iraq's most revered Shi'ite cleric, Grand Ayatollah Ali al-Sistani.
While Abadi is respected by many Iraqis, something few in the country's political elite can claim, a victory narrative can only carry him so far. Even some who plan to vote for Abadi say they're doing it out of pragmatism rather than enthusiasm.
"Abadi is the least terrible option. I want him to remain prime minister so we can have peace and rebuild Iraq," said 32-year-old Ahmed al-Hadi, a supermarket cashier in Baghdad.
