"This is important to us," he told the Rudaw news network. "Saudi Arabia is our neighbour and we cannot continue to live without understanding each other."
Abadi went on to point out that relations between Baghdad and Riyadh were only restored recently since their severing all the way back in 1990 following Saddam Hussein's invasion of Kuwait.
"But today, we need to expand and renew those relations. We should not live in the past," Iraq's prime minister insisted. "There are tensions, and some on both sides don't want these ties to normalise, but we need to work together and bring the relations down to all levels so that they benefit us all."
In another recent interview he said that normalisation of ties with Riyadh was still in the early stages.
The Saudi embassy was reopened in Baghdad for the first time in 25 years in early 2016. A few months later, Baghdad asked Riyadh to replace its ambassador, Thamer al-Sabhan, after he urged Iraq to exclude the Shia-majority Hashd al-Shaabi Popular Mobilisation paramilitaries from the war against the Islamic State group.
|The Iraq-Saudi Arabia border is not the friendliest place [AFP]|
Riyadh subsequently withdrew Sabhan and replaced him with a chargé d'affaires rather than another ambassador. In February, the Saudis said a new ambassador would be assigned to Baghdad - a possible indication that they also don't seek to downgrade bilateral relations.
The Saudis were also concerned about security in Baghdad, saying Shia groups were threatening them. But they sought to stress that the Iraqi people gave them "love and compassion" were "keen on cooperation between Riyadh and Baghdad".
Saudi Foreign Minister Abdel al-Jubeir visited Baghdad in February, the first visit by the Saudi foreign minister since 2003. He emphasised the joint interest the two countries in eradicating IS.
But late last month, Iraqi Foreign Minister Ibrahim al-Ja'afari said that Baghdad would never end its relations with Tehran to placate its Sunni Arab neighbours.
"Iraq is not ready to step towards agitating the region and will not sever ties with any neighbouring country," he declared.
Interestingly, Ja'afari's defence of Baghdad's relations with Tehran to its Sunni Arab neighbours comes just a few months after Iraq's autonomous Kurdistan Region was warned by Tehran over its relations with Riyadh, which opened a consulate in Erbil in February 2016.
Tehran claimed, rather erroneously, that the Saudi embassy in Kurdistan was directly aiding and abetting Kurdish groups fighting the Iranian regime. Erbil meanwhile asserted its right to have relations with any country in the region, and denounced Iran's interference in Kurdish affairs.
|Iraq's relations with Iran have placed it in a good position to mediate between Tehran and Riyadh|
Iraq, a Shia-majority country, is perceived by some in the region's Sunni-majority states as a proxy of Shia-majority Iran. This perception has fundamental flaws. Prime Minister Abadi even went so far as to say that: "The Saudi mentality that Iraq is under Iran's control [is] flat wrong."
Iraq's relations with Iran have placed it in a good position to mediate between Tehran and Riyadh, whose relations hit a new low in January 2016 - when the Saudis executed the Shia cleric Nimr al-Nimr and an Iranian mob ransacked the Saudi embassy in Tehran in response.
Ja'afari was quoted in the Iranian press last January discussing Baghdad's willingness to mediate between Riyadh and Tehran. He said Baghdad had a self-interest in brokering a thaw between the two regional powers "because any crisis in Iranian-Saudi relations affects Iraq as well, and a rapprochement between them would also benefit Iraq".
Under Saddam, Iraq was supported financially by the Saudis and other Gulf states in its eight year (1980-88) war with Iran - which they feared would export its Islamic revolution across the region and depose their regimes - but quickly became a pariah state after its August 1990 invasion of Kuwait.
|The Saudis have been urged to write off the remainder of Iraq's debt to help stabilise Iraq, ravaged by years of war|
Iraq is still in debt to Saudi Arabia from then and owes war reparations to Kuwait, even though these debts were incurred by a harsh authoritarian regime which brutally oppressed those who govern the Iraq today.
The Saudis have been urged to write off the remainder of Iraq's debt to help stabilise Iraq, ravaged by years of war. The Saudis deny that they are considering doing so. However, it would be an honourable thing to do, and would signify they were ready to restart relations on good terms and prepare the ground for a fresh start.
The Saudis, and other regional Sunni Arab states, were extremely slow to accept the new, predominantly Shia, order in Baghdad brought about by the US-led military overthrow of Saddam in 2003. The 2003 regime change was a key year of change in Iraq, which the Saudis did not recognise and adapt to accordingly.
"Saudi Arabia has refused to accept the change and dealt with the new Shiia reality in Iraq with suspicion and mistrust," noted Al Monitor columnist Ali Mamouri.
"Following the IS threat, Iran was one of the first that volunteered and supported all Iraqi parties, including the Kurdistan Regional Government (KRG), the central government and the Sunni factions fighting against IS alongside government forces.
"[In] the absence of a prominent presence of the regional Sunni power represented by Saudi Arabia and Turkey, it goes without saying that this path would lead to a greater Iranian influence in Iraq in the post-IS era."
Mamouri's assessment makes clear that it is in Riyadh's self-interest to normalise relations with Iraq. After all, Riyadh cannot realistically expect to influence Iraqi policy if it doesn't have serious bilateral relations with Baghdad.
An Iraq playing mediator between Riyadh and Tehran could also enable both powers to diplomatically work to reduce tensions in the region's numerous combustible flash-points, where they are both supporting opposing local forces.
Consequently, full normalisation of ties between Baghdad and Riyadh is of great importance to the region's stability and should therefore be strongly supported and encouraged.