The 55-year-old mullah, whose real name is Najmeddine Faraj Ahmad and who has lived in Norway since 1991, has pleaded not guilty to threatening the life of Erna Solberg, an ex-minister who signed his expulsion order in 2003 because he was considered a threat to national security.
Krekar's name is on terrorist lists drawn up by the United Nations and the United States.
His deportation process began in 2003 but has yet to be carried out since Norwegian law prevents him from being deported to Iraq until his safety can be guaranteed and as long as he risks the death penalty.
"Norway will pay a heavy price for my death," he said during a meeting with international media in June 2010.
"If for example Erna Solberg deports me and I die as a result, she will suffer the same fate," he said in Arabic, adding: "I don't know who will kill her: Al-Qaeda, Ansar al-Islam, my family, my children. I don't know... But she will pay the price."
According to prosecutor Marit Bakkevig, the comments were an attempt to get Norwegian authorities to reverse the expulsion order.
Krekar is also accused of threatening other Kurds living in Norway who had burned pages of the Koran, as well as calling for attacks on US soldiers in Iraq on several occasions.
The mullah has admitted to making the statements but has claimed his words merely referred to Islamic principles.
His lawyer Brynjar Meling said he would call for his client's acquittal in court on Wednesday.
"He considers that what he said falls entirely within the laws of freedomof expression and religion," Meling told TV2 news channel.
A date for the verdict has yet to be announced.
While Krekar acknowledges having co-founded Ansar al-Islam, which also figures on international lists of terrorist groups, in 2001, he insists he has not led the group since 2002.