"As we saw so tragically in Paris last week, Iraq is on the front lines of a global conflict," Allen said at a news conference in Baghdad, referring to violence including attacks on satirical weekly Charlie Hebdo and a Jewish supermarket which killed a total of 17 people.
The Islamic State (IS) group's "dark, violent ideology has a long reach," also inspiring militants to carry out attacks in Sydney, Ottawa and Brussels, said Allen, who is coordinating international efforts against the jihadists.
"None of us can afford to say that degrading and defeating Daesh is solely an Iraqi responsibility. Daesh is a global threat. It demands a global response," he said, using an Arabic acronym for IS.
The jihadist group spearheaded a lightning offensive in June that overran much of Iraq's Sunni Arab heartland north and west of Baghdad.
It later turned its attention to forces from Iraq's autonomous Kurdish region, driving them back towards their capital in an attack that helped trigger a US-led air war against IS.
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Allen said that eight countries were carrying out strikes against IS in Iraq, while 12 have pledged to train the country's security forces.
The US and allied countries aim to eventually train 5,000 federal and Kurdish forces every six to eight weeks at five training sites in various parts of Iraq.
But it remains to be seen whether the relatively brief programme will be enough, and if the security forces continue training to maintain newly acquired skills.
Iraqi federal forces, Kurdish troops, Shiite militiamen and Sunni tribesmen are all fighting against IS in Iraq, and have regained some ground from the jihadists.
But three major cities and swathes of other territory remain outside government control.