The programme in question was a panel discussion and was broadcast live by SR International's Somali service.
The police report was filed by Erik Johansson, at the Swedish Evangelical Mission (Evangeliska Fosterlands-Stiftelsen - EFS), after friends told him of the imam's words underlining every Muslim's responsibility to kill anyone who leaves Islam.
"I received a call from my Somali friends who had heard the programme. I don't speak the language myself and when they explained to me, I concluded that this wasn't a message which should be on an SR channel," Erik Johansson told The Local on Thursday.
Johansson also contacted Sveriges Radio in order to register his dismay that the item was left available on their website for more than two weeks. Soon after his telephone call the programme was removed from the website.
In a comment to the Christian website Dagen on Tuesday, SR International head Ingemar Löfgren said that he decided to pull the transcript from SR's website pending receipt of an official translation, pointing out that he is responsible for several channels broadcast in languages which he does not speak.
"If an imam calls for other Muslims to kill converts, then we have a journalistic responsibility... If he didn't get any follow up questions then we have failed in our journalistic responsibility," he said.
According to Erik Johansson, the journalist reminded the imam that they were in Sweden, to which he replied that the same rules apply there.
"It is my hope my police report will encourage them (SR) to change their routines," Erik Johansson told The Local.
The Local's attempts to reach Sveriges Radio International for comment on Thursday have so far been unsuccessful.