Iraqi Prime Minister Haidar al-Abadi visited Iran, when the US and Saudi Arabia most explicitly disagreed with the Iran-Iraq close ties. However, US Secretary of State Rex Tillerson chose a more diplomatic tone; he conceded that the long border between the two countries makes close economic, political, cultural, and soil ties inevitable, but he also warned against Iran's leverage.
Considering the mutual animosity between the US and Iran, the advice is quite comprehensible; however, the main point here is that neither Iran nor the US is entitled to ask an independent country to be in sync with their tendencies and preferences, even if Iraq has perforce to have casual friendly ties with the US due to its role in toppling Saddam Hussein, the former dictator in Iraq, and even if Baghdad feels it is Iran's debt thanks to its unrivalled supports for Iraq against Daesh.
Nonetheless, contrary to US and Saudi complaints against Iran's undeniable leverage in Iraq, what is authentic is the great respect Iran has for Iraq's national sovereignty and territorial integrity, and also Iraqi statesmen's rights to set up their own foreign policy relations, whose proof can be Iran's reactions to Baghdad-Washington ties, Iraqi authorities' visit to Riyadh and their agreement with the Saudis to create a coordinating committee.
Iran understands that, despite Saudi Arabia's role in creation of Daesh and the damage to Iraq, Baghdad has the right to welcome the improvement in ties with Saudi Arabia, as one of the three influential Arab countries, and not to ask for the return of tensions in their ties.
Of course, al-Abadi visited Tehran after each visit to Riyadh, which sends out a clear message, i.e. to assure that Iraq will not form any special relations with the country that created Daesh and is presently opposing Iran, and what is going on between Iraq and Saudi Arabia just pertains to Arab solidarity and diplomatic and good-neighborly etiquette.
While Iran and Iraq's economy, politics, security relations are interwoven, and Saudi Arabia has a lower share of economic ties with Iraq, Tehran has never urged Baghdad to follow the former's policies regarding bilateral relations with Saudi Arabia and the US.
Now, if this is called 'influence', it could be better that Washington and Riyadh pursue a respectful interpretation of 'influence' similar to Iran's in their international relations.
*Fereydoon Majlesi is an expert on Internatonal Relations