US President Barack Obama has warned Iran it could end up fighting sectarian fury “in a whole lot of places” unless it helped stabilise Iraq and pushed for an inclusive, multi-ethnic government.

Shi’ite Iran could play a “constructive” role in helping ease the crisis in Iraq sparked by the lightning advance of Sunni radicals from the Islamic State of Iraq and the Levant (ISIL), Obama said.

But he cautioned that “old habits die hard,” following several days of manoeuvring between Tehran and Washington over possible co-operation amid signs both sides may have a common interest in preventing Iraq’s plight from worsening.

Obama’s intervention came as he announced the dispatch of 300 military advisers to help assess training needs for Baghdad’s armed forces but insisted that he was not getting drawn back into a war Washington launched to topple Saddam Hussein in 2003 and which he declared over in 2011.

“Our view is that Iran can play a constructive role if it is helping to send the same message to the Iraqi government that we’re sending,” Obama said.

That message is that Iraq will only hold together if it becomes an “inclusive” nation where the interests of Sunnis, Shias and Kurds are all respected.

“If Iran is coming in solely as an armed force on behalf of the Shia, and if it is framed in that fashion, then that probably worsens the situation,” Obama said.

“Iran obviously should consider the fact that if its view of the region is solely through sectarian frames, they could find themselves fighting in a whole lot of places.”

Earlier suggestions by Secretary of State John Kerry that Washington could even seek Iran’s military co-operation caused a political row on Obama’s right flank – and a hurried clarification that the administration saw no chance the two sworn foes could fight on the same side.

Obama took pains to underscore deep differences with the Islamic republic, despite his efforts to conclude a deal on rein in Tehran’s nuclear program.

He criticised Iran for “coming in hot and heavy” on the side of Syria’s President Bashar al-Assad in his bloody civil war with opposition groups.

But the sudden success of ISIL extremists, including the capture of the country’s second largest city of Mosul, alarmed leaders in Tehran and Washington.

Both governments, for their own reasons, oppose the rise of the Sunni insurgents and have a common interest in seeing the Baghdad government fend off the Al-Qaeda inspired forces.

The two nations, bitter foes for more than 30 years, held brief talks this week in Vienna on the sidelines of international consultations on Iran’s nuclear program.