Meeting with a group of senior editors on the first day of the United Nations General Assembly gathering of world leaders, Rouhani stressed that Iran condemns the Islamic State group, although he did not single them out by that name and referred to only as "terrorists", for trampling on human rights and torturing and killing civilians.
He said Iran stands ready to help fight terrorism.
But Rouhani said the US policy is confused because it simultaneously opposes the militants while also trying to undermine the government of Syria's President Bashar Assad.
He suggested Washington now faces a challenge with its "time management" and should consider the goal of fighting the terrorists first and address its issues with the Syrian government later.
Nighttime raids began yesterday on Islamic State militants in Syria, as US-Arab airstrikes hit the group's military strongholds in both Syria and Iraq.
Syria's Foreign Ministry said the US informed Syria's envoy to the UN that strikes would be launched in Syria.
The US and Iran have been unable to work together to combat the Islamic State group, complicating efforts against militants that both Washington and Tehran see as a threat.
Iran's supreme leader, Ayatollah Ali Khamenei, who has the final say on all state matters, decisively ruled out an alliance. He said Iran had rejected an invitation by US Secretary of State John Kerry to discuss cooperation.
The United States, meanwhile, feared that bringing Iran into the fight could bolster its influence in Iraq.
Washington and Tehran were nonetheless in back-room contacts about cooperation for weeks. Some moderate voices in Iran's diplomatic circles supported an alliance with the US against the militants.
Any military cooperation and coordination between Iran and the United States is complex because the two countries have had relations frozen since shortly after the 1979 Islamic Revolution and do not have official diplomatic ties.
