Washington (CNN) Secretary of State John Kerry acknowledged for the first time that the U.S. is having talks with Iran that could include a possible prisoner swap, in an interview with CNN's Elise Labott that aired Wednesday.

Iranian President Hassan Rouhani also recently told CNN that the two countries are talking, and laid out his terms for such a deal. Iran and the U.S. recently struck a nuclear agreement meant to curb the country's nuclear ambitions.

Asked if talks on the Americans being held were making progress, Kerry said he has "raised them in all of our sessions. We've had a lot of conversations. We are continuing those conversations now."

Kerry did not reject the idea of a swap, though he would not discuss the details of the ongoing conversations, saying only, "I am hopeful that the day will come soon -- obviously sooner rather than later -- but soon when all of our citizens can come home."

There are three Americans known to be held in Iran: Washington Post journalist and dual Iranian-American citizen Jason Rezaian; Amir Hekmati, a former Marine; and Saeed Abedini, an Iran-born American Christian pastor. In addition, Robert Levinson, a former FBI agent and contractor for the CIA, who is missing after visiting the country in 2007. Iranian officials have denied any knowledge of Levinson's whereabouts.

In a portion of the interview that aired Tuesday, Kerry called Russian President Vladimir Putin's involvement in Syria a possible "opportunity" for the United States.

Yet his message sounded somewhat different the next day after Russia carried out a bombing mission Wednesday inside Syria that may not have targeted ISIS, according to a senior U.S. administration official. Instead, some have said the moves seem more indicative of support for Syrian President Bashar al-Assad, whom the U.S. has called on to leave office.

Speaking Wednesday at a U.N. Security Council meeting, Kerry warned that while the U.S. welcomes "genuine efforts" to fight ISIS, also known as ISIL, "we must not be confused in our fight against ISIL with support for Assad."

"Moreover, we have also made clear that we would have grave concerns should Russia strike areas where ISIL and al Qaeda affiliated targets are not operating," he added. "Strikes of that kind would question Russia's real intentions fighting ISIL or protecting the Assad regime."

Kerry insisted that U.S.-led airstikes against ISIS in Syria "will continue" undeterred, regardless of Russian actions in the same skies.

On Tuesday, Kerry predicted to CNN that Russia's presence in Syria means Moscow could find itself in a "complicated" situation that could affect its policy toward the war-torn country and its leader, President Bashar al-Assad.

"If he's going to side with Assad and with Iran and Hezbollah, he's going to have a very serious problem with the Sunni countries in the region," Kerry said of Putin. "That means he ... could very well become a target for those Sunni jihadists."

Kerry explained: "It's an opportunity for us to force this question of how you actually resolve the question of Syria. And the bottom line is, you cannot resolve it without including the Sunni(s) in a political solution, a political agreement ultimately, and that will mean that you're going to have to have some kind of transition, some kind of timing. Because as long as Assad is there, you simply can't make peace. Period."

Kerry also said that Syrian President Bashar al-Assad must leave as part of an "orderly transition," rather than calling for his immediate ouster, marking a change in the U.S. position.

He added that if Assad left more quickly, it could lead to an "implosion" that would strip the country of any civil life. He added that Assad has a "complete lack of legitimacy" as leader given that three-quarters of Syrians "have already voted with their feet" by moving elsewhere from Assad-ruled territory.

"We need to have an orderly transition, a managed transition, so that you don't have a fear for retribution, loss of life, revenge," Kerry said, urging a leadership change over a "reasonable period of time" but declining to be more specific.

Kerry is in New York for the United Nations General Assembly this week as the U.S. met with leaders from Iran and Cuba as well as Russia. Kerry is scheduled to meet throughout the day with Russian Foreign Minister Sergey Lavrov after Russia commenced airstrikes in Syria.

The current secretary of state also pushed back on criticisms that his department has been slow to release works email from his predecessor, Hillary Clinton, who maintained a private email server while working for the State Department.

"We cannibalized the different bureaus to bring people from those bureaus and put them to work to help do this. But it takes an experienced eye to read the cable and know whether or not it should or should not be classified," Kerry said. "So that's what we're doing and I think we will be ahead of the curve."

Kerry also praised his staff for meticulously going through her work emails in order to prevent classified information from being released.

"We have an obligation to review what is classified information and what is not. And if any other department in the government is mentioned in a particular email it has to go to that department in order for them to be able to clear it. So it's by nature a cumbersome process," he said, twice declining to answer whether the exercise was a "sideshow."