According to al-Forat news website, Iran’s Ambassador to Iraq Hassan Danaeifar conveyed the message to al-Abadi.
In this message, President Rouhani thanked the Iraqi government for making "significant efforts” to ensure the safety of Arbaeen pilgrims and appreciated the "devoted and patient” nation of Iraq for hosting and serving the pilgrims.
Arbaeen marks the 40th day after the martyrdom anniversary of the third Shia Imam, Imam Hussein (AS) and his faithful companions in the 680AD battle of Karbala.
Some 27 million Shia pilgrims from over 60 countries converged on Karbala last week to take part in Arbaeen mourning rituals.
There were around 3 million Iranians among those who went to the holy city for Arbaeen this year.