It was the first strike inside Syria claimed by Iraq since the three-year uprising against President Bashar al-Assad erupted in March 2011.
The conflict has spilled across the border, contributing to a dramatic rise of violence in Iraq since the country's 2006-2008 sectarian war.
Meanwhile, Iraqis living overseas began voting ahead of Wednesday's general election that will see Prime Minister Nuri al-Maliki seeking a third term despite worsening sectarian tensions at home, rampant corruption and high unemployment.
Sunni radicals ISIL emerged in Iraq in the wake of the US-led invasion in 2003, and later expanded into Syria during the uprising against Assad.
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Maan said "there was no coordination with the Syrian regime" over the strike.
"Our responsibility now is to protect our border and to protect the border from the other side, because there is no protection from the other side," he said.
Fighters from ISIL and other militants control the city of Fallujah in Anbar, just a short drive from Baghdad, and security officials have voiced worry that the group is seeking to encroach on the capital as well.
Illustrating those concerns, ISIL on Friday set off twin bombings against a Shiite political rally, killing 36 people.
The latest show of force by the government security forces came as voting opened for Iraqis living in 29 countries overseas, including substantial contingents in Britain, Sweden, Jordan, Iran and Germany.
Out of country voting will run today and tomorrow. Prisons and hospitals as well as members of Iraq's security forces will cast their ballots tomorrow as well ahead of Wednesday's poll.