In an interview in Tehran with NBC News, Rouhani reiterated Iran's stance that "under no circumstances would we seek any weapons of mass destruction, including nuclear weapons, nor will we ever."
"We have never pursued or sought a nuclear bomb, and we are not going to do so," he said. "We solely are looking for peaceful nuclear technology."
The new leader of the Islamic republic said he wields the power to reach an agreement that will mollify the United States and other nations concerned about Iran's nuclear ambitions.
"In its nuclear program, this government enters with full power and has complete authority," Rouhani said.
"The problem won't be from our side. We have sufficient political latitude to solve this problem."
Rouhani, who has struck a more moderate stance than his predecessor, Mahmoud Ahmadinejad, also said the tone of a letter he received recently from U.S. President Barack Obama expressing a willingness to resolve the issue was "positive and constructive."
"It could be subtle and tiny steps for a very important future," he said. "I believe the leaders in all countries could think in their national interest and they should not be under the influence of pressure groups. I hope to witness such an atmosphere in the future."
Rouhani also spoke to the crisis in Syria, an ally of Iran.
"We are not the government of Syria," he said. "We are one of the countries of this region which is asking for peace and stability and the elimination of all weapons of mass destruction in the entire region."
Asked if he thought Obama appeared weak by not pushing ahead with a military strike against Syria over the Assad regime's alleged use of chemical weapons, Rouhani replied: "We consider war a weakness. Any government or administration that decides to wage a war, we consider a weakness. And any government that decides on peace, we look on it with respect to peace."