"You might see NATO making a contribution to logistics, acquisitions, institutional capacity building, leadership schools, academies -- those kind of things," Dunford, who is Chairman of the US Joint Chiefs of Staff, said.
The issue is at the top of the agenda for next week's summit, with US President Donald Trump pushing the allies to take on a greater role in combatting terrorism.
After months of brutal, street-by-street combat, IS has lost control of most of its stronghold of Mosul in Iraq, while the jihadists have become largely isolated in Raqa in neighboring Syria.
A change in who leads the training mission would likely also mean revamping the nature of the effort, Dunford said.
"We are not talking about NATO doing what we are doing now for combat advising in places like Mosul or Raqa," the general said.
"I don't think we are at the point now where we can envision or discuss NATO taking over" all missions of the anti-IS coalition in Iraq, he added.
NATO's top brass said on Wednesday they believed the alliance should consider joining the anti-Islamic State coalition put together by Washington to fight jihadists in Syria and Iraq.
General Petr Pavel, head of NATO's military committee, told reporters after chiefs of defence staff (CHODS) met in Brussels that it was time to look at this option.
"NATO members are all in the anti-IS coalition. The discussion now is -- is NATO to become a member of that coalition," he said.
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The issue is at the top of the agenda for next week's summit, with US President Donald Trump pushing the allies to take on a greater role in combatting terrorism.
After months of brutal, street-by-street combat, IS has lost control of most of its stronghold of Mosul in Iraq, while the jihadists have become largely isolated in Raqa in neighboring Syria.
A change in who leads the training mission would likely also mean revamping the nature of the effort, Dunford said.
"We are not talking about NATO doing what we are doing now for combat advising in places like Mosul or Raqa," the general said.
"I don't think we are at the point now where we can envision or discuss NATO taking over" all missions of the anti-IS coalition in Iraq, he added.
NATO's top brass said on Wednesday they believed the alliance should consider joining the anti-Islamic State coalition put together by Washington to fight jihadists in Syria and Iraq.
General Petr Pavel, head of NATO's military committee, told reporters after chiefs of defence staff (CHODS) met in Brussels that it was time to look at this option.
"NATO members are all in the anti-IS coalition. The discussion now is -- is NATO to become a member of that coalition," he said.
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