Iran imposed travel bans on 15 people for alleged involvement in a leaked audio recording in which the foreign minister complains about the influence of the Revolutionary Guards on Iranian diplomacy, a semi-official news agency said on Thursday.

In the leaked interview, aired by the London-based Iran International Persian-language satellite news channel late on Sunday, Foreign Minister Mohammad Javad Zarif said he had "zero" influence over Iran's foreign policy. 

"According to a judiciary source, 15 people involved in the interview have been banned from leaving Iran," the semi-official ISNA news agency reported.

The recording, shedding a rare light on ties between the government and the elite Guards, has angered hardliners in Iran, who called the leak "an espionage act". Some lawmakers have called for Zarif's resignation.

President Hassan Rouhani on Thursday replaced the head of the state-run think-tank that was in charge of conducting the interview. Authorities have said the recording was part of a wider project with government officials and was produced for state records rather than for publication.

"Hessameddin Ashena, head of the Strategic Studies Centre, had resigned, President Rouhani has appointed the cabinet spokesman Ali Rabiei to replace him," state news agency IRNA reported.

Ashena, who Iranian media said was present during the seven-hour interview with Zarif, is also an adviser to the president.

Ordering an inquiry into the recording's release, Rouhani said on Wednesday the leak was intended to disrupt talks between Tehran and six powers in Vienna aimed at reviving a 2015 nuclear deal that Washington abandoned three years ago. 

While on a regional tour, Zarif said in an Instagram post that he regretted the leak and his remarks were misinterpreted. The news channel only published three hours of the interview.

Using language rarely heard in politics in Iran, Zarif said in the interview that the then leader of the Guards' clandestine overseas Quds Force, Qassem Soleimani, had tried to spoil the nuclear deal by colluding with Russia.

Soleimani was killed in a U.S. drone attack in Iraq last year. Iran retaliated with a rocket attack on an Iraqi air base where U.S. forces were stationed.

Although Zarif has repeatedly said he has no intention of running in Iran's June 18 presidential election, his name has been suggested by moderates as a possible candidate for the election, in which several prominent Guards commanders are also running for the top executive post.

Some critics said Zarif's comments in the leaked tape were aimed at attracting votes from Iranians disillusioned by a stalled economy and lack of political and social freedoms.

(With input from agencies)