Retired Gen. John Allen, appointed by US President Barack Obama to build a coalition against Islamic State, told a conference in Qatar the group was not merely an Iraqi problem or a Syrian problem but "a regional problem trending towards global implications".
The group has lost about a quarter of the populated areas it once held in Iraq, but countering its ideology might take a generation or more, he told the Brookings Institution's US-Islamic World Forum.
Last month, the Iraqi government had its worst military setback in nearly a year when Islamic State seized Ramadi from a weakened Iraqi army. The capital of the overwhelmingly Sunni Muslim province of Anbar is 90 km (55 miles) west of Baghdad.
Since then, government troops and allied Shi'ite Muslim militia have been building up positions around Ramadi. Many Iraqi Sunnis dislike the ultra-hardline Islamic State but also fear the Shi'ite militias after years of sectarian strife.
Allen said there was no future for Iraq without Sunni support and stressed the need for the government to control the Shi'ite militias, some of whom have links to Iran.
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"We said many times that it is critical that all forces in the battle field must be under the command and control of the government of Iraq for the counter-ISIL operation to be successful," he added, using a common acronym for Islamic State.
Washington remained "very attentive and concerned about extremist militia elements frequently influenced by Iranian leadership, where Iran may play a significant role in their presence," he said.
He added that Turkey's borders with Syria and Iraq were the "last line of defence" against foreign fighters coming into the conflict - but other countries also needed to help stop the influx.
Syrian President Bashar al-Assad should have no place in a solution to Syria's war, he added, repeating Washington's stance on efforts to end the fighting.
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