"Putin told me Russia fighting ISIS in Syria and I trust him, I'm open to Russian airstrikes vs Daech [Islamic State] in Iraq," al-Abadi is quoted as saying by France 24 on Twitter.
According to the minister, Iraq is "not getting massive US military support" against the group. "We need a broad coalition including Russia and Iran," he said.
A US-led coalition has been bombing ISIL targets in Iraq and Syria since 2014.
On Wednesday, Russian parliament authorized the use of the country's Air Force in fight against ISIL in Syria, following a request by President Bashar Assad.