"I believe we didn't have sufficient time to really coordinate the meeting to the full extent that we needed to," Rouhani told CNN.
Given that U.S. and Iranian leaders have not met face-to-face for 35 years, he said, "we must give time for diplomacy to work itself, for dialogue to come about, for circumstances to be laid properly."
Still, the two men recently exchanged letters, and Rouhani said the ice is "already beginning to break because the environment is changing and that has come about as a result of the will of the people of Iran to create a new era of relations between the people of Iran and the rest of the world."
Resolving the standoff over Iran's nuclear program is the priority, he said. "If the nuclear issue is settled conclusively, I believe that that will pave the way for numerous other issues that can be discussed."
Iran insists its program is for energy purposes; the United States and several other countries believe it could be a guise for building nuclear weaponry.
Rouhani also called for sanctions against his country to be lifted.
Rouhani said he has full permission from Iran's supreme leader, Ayatollah Ali Khamenei, to negotiate with the West.
"I think that the president of Iran has the authority whenever the national interest of the country is involved," Rouhani told Amanpour. "The supreme leader of Iran has said that should negotiations be necessary for the national interest of the country, he is in fact not opposed to it."
"Now, if an opportunity was created today, had arisen today," the Iranian president said, "and the prep work for that had been done, most probably the talks would have haven taken place, primarily focused on the nuclear issue or the developments on the Middle East. Therefore the supreme leader, I can tell you, has given permission for my government to freely negotiate on these issues."
Rouhani: Social media may be coming to Iran
An irony surrounding Rouhani's leadership is that his office tweets and posts on Facebook -- even though those social media platforms are banned in Iran.
"All my efforts are geared to ensure that the people of Iran will comfortably be able to access all information globally and to use it," he told CNN. "There are large social networks at a global level around today. And I believe that all human beings have a right, and all nations have a right to use them."
He also noted that some countries including Iran have "ethical frameworks" that they try to follow.
The Iranian government needs "to be open to criticism" expressed through social media, he said. "So one of my plans is to reduce the problems that people face currently on these issues, so that within those sort of moral frameworks that we have for ourselves, that we are able to access these social network sites."