During a meeting with Germany's visiting foreign minister, Abadi stressed the "importance of stopping oil smuggling by (IS) terrorist gangs, the majority of which is smuggled via Turkey," a statement from his office said.
Relations with Ankara have improved since Abadi took office in 2014, but tensions remain over issues including the Syrian civil war, and more recently a row over a Turkish military deployment in northern Iraq.
It is the latest in a series of accusations linking Turkey and oil smuggling by IS, which overran large parts of Iraq last year and also holds major territory in neighbouring Syria.
Russia accused Turkish President Recep Tayyip Erdogan and his family of involvement in the IS oil trade, to which he responded that Russia was in fact involved.
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Iranian media then picked up Russia's claims, prompting Erdogan to lash out at his Iranian counterpart.
And Mohsen Rezaie, secretary of Iran's Expediency Council, said Iranian military advisors on the ground in Iraq and Syria had images of IS oil trucks going to Turkey.
The US has meanwhile said that IS oil smuggling through Turkey is not significant, prompting Moscow to accuse Washington of a cover-up.
Iran and Russia are open backers of Syrian President Bashar al-Assad's regime, while Turkey supports rebels seeking his overthrow and the US has also called for him to leave power, but is more directly concerned with IS.
Baghdad has close ties to Iran and is viewed as sympathetic to Assad, and various Iraqi militia groups have fought in Syria on his behalf, but Iraq has sought to avoid publicly taking sides in the conflict.
In recent days, Baghdad has accused Ankara of sending troops to northern Iraq, where Turkey has been training anti-IS forces, without its knowledge or approval and demanded they be withdrawn.