The Iranian leader also said he listened carefully to Obama's speech and hoped the United States "will refrain from following the shortsighted interests of warmongering pressure groups" so the two nations "can arrive at a framework to manage our differences."
In February, the bloc of countries leading the diplomatic effort offered Iran a package of economic incentives to abandon its nuclear ambitions.
In exchange for easing of sanctions barring trade with Iran in gold and other precious metals, the group wants Iran to shut its underground enrichment facility at Fordo, near the holy city of Qom, and ship out its stockpile of uranium enriched to 20% purity.
The group also proposed fuel for a medical reactor and easing sanctions on aviation spare parts in exchange for Iran suspending its uranium enrichment and shipping its stockpiles out of the country.
Iran has never formally responded to the deal and it remains to be seen whether the group would be willing to sweeten the offer in the new climate.
Rouhani told CNN's Christiane Amanpour that he has the full backing of Iran's supreme leader, Ayatollah Khamenei.
"The supreme leader, I can tell you, has given permission for my government to freely negotiate on these issues," he said in the interview. Obama administration officials have said they believe the Iranians are ready to negotiate because of the toll international sanctions have taken on their economy.
In his remarks Thursday, Rouhani said Iran would be willing to live under International Atomic Energy Agency safeguards against nuclear weapons, but scolded Israel for not signing on to international nuclear nonprofileration agreements.
"Israel, the only nonparty to the Non-Proliferation Treaty in this region, should join thereto without any further delay. Accordingly, all nuclear activities in the region should be subject to the IAEA comprehensive safeguards," he said.
"The international community has to redouble its efforts in support of the establishment of this zone. This would constitute a contribution to the objective of nuclear disarmament."
Israel has never acknowledged having nuclear weapons but is widely believed to possess them.
Israeli officials fear Iranian nuclear weapons pose a direct threat to their security, especially after years of bellicose rhetoric from the previous Iranian president, Mahmoud Ahmadinejad.
While Rouhani's tone has been different -- he recently wished Jews a happy Rosh Hashanah through his official Twitter account and on Wednesday acknowledged the reality of the Holocaust in Western media interviews -- Israeli Prime Minister Benjamin Netanyahu said earlier this week that he's not yet sold on Iran's seemingly more moderate tone.