"If the Americans take the appropriate steps and set them free, certainly the right environment will be open and the right circumstances will be created for us to do everything within our power and our purview to bring about the swiftest freedom for the Americans held in Iran as well," Iranian President Hassan Rouhani told CNN's Christiane Amanpour on Sunday.
Rouhani said that anytime something can be done to help someone in prison, "nothing would make me happier."
There are three Americans known to be held in Iran and one who is missing after visiting the country.
Rezaian, a dual Iranian-American citizen, has been held in Iran for more than a year after being arrested and charged with "espionage and other offenses." His trial has been held behind closed doors.
The others known to be held in Iran are Amir Hekmati, a former Marine sentenced to death in January 2012 for espionage, waging war against God and corrupting the earth, according to the Free Amir website set up by his supporters; and Saeed Abedini, an Iran-born American Christian pastor who was detained in Iran in 2012, according to the American Center for Law and Justice, and sentenced to eight years in prison on charges of attempting to undermine the Iranian government.
The fourth American is contractor Robert Levinson, a former FBI agent and contractor for the CIA, who vanished after visiting Iran in 2007. Iranian officials have denied any knowledge of his whereabouts.
Because Iran has reached a landmark nuclear agreement with world powers, Rouhani said, there is no reason for the U.S. to hold prisoners who were arrested for violating the sanctions that are now being lifted.
"There are a number of Iranians in the United States who are imprisoned, who went to prison as a result of activities related to the nuclear industry in Iran," he said through an interpreter.
"Once these sanctions have been lifted, why keep those folks in American prisons?"
"So they must be freed."
Rouhani said that "consular issues" had been discussed on the sidelines of the nuclear negotiations, and that it would not be unusual for those talks to now continue.
"If the Americans take the appropriate actions vis-a-vis Iranian citizens who are being imprisoned here, then the right atmosphere and environment will be created for reciprocal action perhaps."
Secretary of State John Kerry, who is in New York for this week's meeting of the U.N. General Assembly, was asked later Sunday whether he would support such an exchange.
"I have yet to hear directly from the Iranians on anything direct," Kerry told reporters. "We've had some conversations but ... we'll wait and see where we are."