Rowhani said that should extend to "all rights of the Iranian nation, particularly nuclear rights and the right to enrich uranium on its territory within the framework of international rules".
His comments, at an annual military parade, came on the eve of his departure for the UN General Assembly in New York where he is scheduled to meet French President Francois Hollande on the sidelines.
"If they (Western governments) accept these rights, the Iranian people are a rational people, peaceful and friendly. We stand ready to cooperate and together we can settle all the region's problems and even global ones," Rowhani said.
Iran claims the right to enrich uranium for peaceful purposes under the terms of the nuclear Non-Proliferation Treaty.
But the UN Security Council has imposed successive rounds of sanctions on Iran for failing to heed ultimatums to suspend the sensitive activity, which Western governments suspect conceals a covert drive for a weapons capability.
Rowhani, a moderate on Iran's political scene, has made several diplomatic overtures since his election in June, and there has been speculation that he could also meet US President Barack Obama on the sidelines of the General Assembly, which opens on Tuesday.