Few issues have inspired more vitriol this summer than the historic agreement between Iran and six world powers: the United States, Russia, China, Britain, France and Germany. The deal drastically curtails Iran's nuclear program in exchange for the lifting of economic sanctions.

Depending on where you stand politically, it's either a triumph of global diplomacy, the best available solution or a blunder of epic proportions. Over the past few months, nearly everyone has weighed in from President Obama and the Congress, to Republican and Democratic presidential candidates to Israeli Prime Minister Benjamin Netanyahu. But not much has been heard from the Iranians.

With that in mind, we traveled to Tehran last week to sit down with Iranian President Hassan Rouhani, for the first interview he has given to a Western news organization in nearly a year.

Iranian President Hassan Rouhani CBS News

Steve Kroft: What do you think of the agreement?

President Rouhani: A very difficult agreement to reach with lots of ups and downs. But it's the right path we have chosen. I am happy that we have taken extremely important steps on this issue and are in the process of taking the final steps.

Steve Kroft: Were you surprised by the ferocity of the debate in the United States and the outcome?

President Rouhani: It was predictable. An issue of this significance cannot be resolved without its opponents. One is surprised by the commentaries and the commentaries are not very pleasant. Some groups and political parties may be against it, but the governments of the world, all together, welcomed this deal.

Steve Kroft: Opponents have argued that U.S. has given away too much for very little in return from Iran. Agreeing to lift the sanctions on Iran in exchange for, what they call, a temporary 15-year freeze on nuclear operations after which Iran would be free to resume or begin work on a nuclear bomb with far more resources than they have now.

President Rouhani: If a country wanted, with the technical resources it has, to gain an atomic bomb, this deal would have been a very bad deal for it. Because the deal creates limitations from all sides to getting an atomic bomb. But if a country has been after peaceful technology from the beginning, then it has lost nothing. We wanted this incorrect accusation that Iran is after nuclear weapons corrected and resolved and that the goal of Iran is peaceful activity. In this deal, we have accepted limitations for a period of time in order to create more trust with the world.

The whole deal requires a leap of faith between two longtime enemies. The Iranians have always insisted that their nuclear program is peaceful and that a religious fatwah prohibits them from building nuclear weapons. But there is little doubt that the Iranians know how to build them and have had the wherewithal to do it. Now, they will be required to ship 98 percent of their enriched uranium out of the country, lock up thousands of centrifuges, close its bombproof enrichment facility at Fordow, disable its heavy water redactor at Arak, and submit to rigorous international inspections.

The opposition here has also been ferocious. The deal has been attacked on state television and in hardline newspapers and the head of the Revolutionary Guard has said, "We will never accept it."

Steve Kroft: The United States seems to have its hardliners and Iran seems to have its hardliners. The opponents say essentially that they think Iran has given up too much control over their nuclear program to the U.S. and other foreign countries, and to the IAEA. Do you see similarities between the United States and Iran in terms of the opposition to this?

President Rouhani: There are similarities. It's natural that opponents always look for the maximum possible outcome. In an agreement, neither achieves the maximum. Both sides must always concede a little bit from the maximum to get an agreement. Therefore, the person who seeks the maximum complains. The result of this agreement benefits everyone, benefits both sides, because we have been able to reach an understanding, an agreement, on a very complicated issue at the negotiating table and be able to prevent misunderstandings, and take the first step towards trust. Of course, for reaching trust between the U.S. and Iran, there is need for a lot of time.

Steve Kroft: Some of the opponents are very powerful. The commander of the Revolutionary Guards, for example, has condemned the deal. How do you deal with that? That's an important political force in this country.

Iranian President Hassan Rouhani with Steve Kroft Aaron Tomlinson

President Rouhani: It's clear that some will be opposed...some will be in favor, will express their opinions, but at the same time after the agreement is approved by the responsible institutions, everyone will comply with that. The Revolutionary Guards also, when the deal is approved by responsible institutions, they, too, will respect this agreement.

President Rouhani's boss, Supreme Leader Ayatollah Ali Khamenei has final say on the agreement and has sent it to the Iranian Parliament and the Supreme National Security Council on national security for a vigorous debate. Publicly, the ayatollah has maintained a hardline stance against the United States, while supporting the negotiations. President Rouhani expressed confidence that the deal will be approved.

President Rouhani: The majority of our people, in opinion polls, have a positive view of the agreement. And usually institutions like the parliament and the Supreme National Security Council, are usually not far-removed from public opinion and move in that direction.

Steve Kroft: You have been very temperate in your statements about these negotiations. You have been trying to encourage a sense of goodwill between the United States and Iran, but some of this -- some of the success has been undercut by very harsh statements from both sides. Since the deal, the Ayatollah Khamanei has endorsed, even praised, the chanting of "Death to America" and "Death to Israel" at the Friday prayers by demonstrators and he continues to call the United States the "great Satan." Do you believe the United States is the "great Satan?"

President Rouhani: The enmity that existed between the United States and Iran over the decades , the distance, the disagreements, the lack of trust, will not go away soon. What's important is which direction we are heading? Are we heading towards amplifying the enmity or decreasing this enmity? I believe we have taken the first steps towards decreasing this enmity.

Steve Kroft: Do you think the United States is the "great Satan?"

President Rouhani: Satan in our religious parlance is used to refer to that power that tricks others and whose words are not clear words, do not match reality. What I can say is that the U.S. has made many mistakes in the past regarding Iran, and must make up for those mistakes.

Steve Kroft: I'm sure you realize that it is difficult for many Americans to get past the fact that President Obama has signed an agreement with a country that says, "Death to America, Death to Israel." How do you explain this? What are they to make of it? Are they to take it literally? Is this for domestic, internal Iranian political consumption? What are Americans to make of it, the language?

President Rouhani: This slogan that is chanted is not a slogan against the American people. Our people respect the American people. The Iranian people are not looking for war with any country. But at the same time the policies of the United States have been against the national interests of Iranian people. It's understandable that people will demonstrate sensitivity to this issue. When the people rose up against the shah, the United States aggressively supported the shah until the last moments. In the eight-year war with Iraq, the Americans supported Saddam. People will not forget these things. We cannot forget the past, but at the same time our gaze must be towards the future.

Steve Kroft: "Death to America" is very simple concept. Three words, not much room left for interpretation. Not very conciliatory. Do you see the day when that language will not be used? You yourself have encouraged both sides to try and lower the temperature.

President Rouhani: If America puts the enmity aside, if it initiates good will, and if it compensates for the past, the future situation between the United States and Iran will change.

Steve Kroft: The United States has just signed an agreement with Iran to lift the sanctions, is that not a sign of goodwill?

President Rouhani: It hasn't been implemented yet...the lifting of the sanctions must be initiated.

Full implementation of the agreement is still months away and requires that the International Atomic Energy Agency certify that Iran has lived up to its commitments under the deal.

Steve Kroft: Do you think the level of trust between Iran and the United States has improved because of this treaty?

President Rouhani: Relative to the past, it's improved. But this does not mean that all disagreements are resolved, or all the distrust removed, in one case, on one issue, yes, we have managed to overcome the problem.

Steve Kroft: There has been speculation and hope both inside and outside of Iran and in the United States that this nuclear deal could be a catalyst for some broader, if limited, cooperation between the two countries where there are mutual interests.

President Rouhani: Many areas exist where in those areas it's possible that common goals, or common interests, may exist. But what is important is that in the nuclear agreement, we see how the two sides behave in action. Enacting this deal in a good way will create a new environment.

Ayatollah Khamenei has said that there will be no further cooperation beyond the nuclear agreement, but there is already some indirect military coordination between U.S. airstrikes and Iranian-backed Shiite militias both fighting against ISIS in Iraq. Officially, it's being done through the Iraqi military. There is also the possibility of future cooperation in Syria.

Steve Kroft: You have said that you are willing to sit down with any country, friend or enemy, to discuss the situation in Syria in order to stop the bloodshed. What does Iran see as a possible, workable, acceptable solution to the situation in Syria?

President Rouhani: Look, in a county where a large segment of the country has been occupied by terrorists, and there is bloodshed inside the country, millions of people have been displaced, how is it possible that we fight the terrorists of this country without supporting and helping the government of that country? How can we fight the terrorists without the government staying? Of course, after we have fought terrorism and a secure environment is created, then it is time to talk about the constitution, or the future regime to talk and discuss opposition groups and supporters sit at the table, but during a situation of bloodshed and during an occupation of the country, what options exist?

So far, President Rouhani has been the biggest political beneficiary of the agreement between Iran and the United States. He is popular with the voters right now, but he's also ruffled some feathers and, no doubt, irritated political rivals.

Steve Kroft: This agreement was a big political victory for you personally. You were elected president based on the idea that you wanted to open up Iran to the outside world, that you wanted to get the sanctions lifted, that you wanted to bring prosperity back to the country, so Iran can take its place among the great nations of the world and not be isolated. There are still some things in that agenda that are still unfulfilled: freedom of speech, more access to the Internet and personal freedoms.

President Rouhani: I think relative to the two years I've been in office, I have been successful - not 100 percent of course, but successful. Our relations with other countries have improved. There is more freedom at the universities, lively debates and greater freedom of the press, compared to the past. Of course, there are some issues that are not in control of the government.

Two of those issues are human rights and personal freedoms are in the domain of Iran's conservative judicial system. Two former presidential candidates have been under house arrest for the past four and a half years and there are at least three Americans imprisoned here.

Steve Kroft: As we sit here speak the-- right now, there is a dual American/Iranian citizen, a journalist for the Washington Post, Jason Rezaian, in prison for more than a year on unspecified charges. There has been talk among leaders in the last few weeks that there might be a prisoner exchange. Is there anything you can say to clarify the situation?

President Rouhani: We have Iranians who are imprisoned in the United States, Iranians who are being pursued and most of them are being pursued for circumventing the sanctions. And, you know, that from the beginning we considered the sanctions to be wrong, and we encouraged everyone to circumvent them. We consider all those prisoners to be innocent, and consider it wrong that they are in prison.

Steve Kroft: Would you support a prisoner exchange?

President Rouhani: I don't particularly like the word exchange, but from a humanitarian perspective, if we can take a step, we must do it. The American side must take its own steps.

If the nuclear deal stays on track, and the sanctions are lifted, the Iranian treasury will soon begin collecting a $100 billion in oil revenues that have been frozen in overseas banks. And President Rouhani says Iran will be open for business.

President Rouhani: As you know, in Iran, we are transferring the economy step by step to the private, nongovernmental sector. Our private sector and the American private sector can improve the environment. Actually, it will strengthen the nuclear agreement. Even tourism, if the people of the United States come to Iran and see its ancient history and nature of Iran, and the people of Iran go to the United States to see America, this can shorten the walls of mistrust and improve the situation for the future.