"If countries in the region agree, they could eliminate anti-Islamic groups like Daesh and liberate thousands of men, women and children who have lost their homes," Rouhani told an anti-extremism conference in Tehran, using the Arabic acronym for IS.
"In this case, there would be no need for the presence of foreigners," he added.
Iran is a key ally of Syrian President Bashar al-Assad and has said it supports the Iraqi government in its fight against IS.
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A US-led coalition, which includes five Arab states but not Iran, has carried out hundreds of airstrikes on IS, which controls swathes of Iraq and Syria.
The American commander of the war effort said Monday that US allies were ready to send roughly 1,500 security personnel to Iraq to help Baghdad fight the jihadists.
This follows Washington's decision last month to double its military footprint in Iraq to 3,100 troops.
Rouhani called for countries to "stop direct and indirect financial aid to terrorist groups" -- something Iran has frequently declared Qatar and Saudi Arabia guilty of.
He also called for a change in teaching at religious learning centres to prevent young people being radicalised and for the international community to fight "the use of the Internet and social networks by terrorists".