Norwegian intelligence (PST) had arrested Krekar, 63, on Monday in Oslo under an international search warrant as well as an Italian arrest warrant, and an Oslo judge ruled Wednesday he should be placed in provisional detention for four weeks.
Italy's justice ministry meanwhile told Norwegian media that Rome would make an official extradition request.
However the procedure could take years as Krekar's lawyers say they will appeal a 12-year sentence which a court in Bolzano, northern Italy, handed down in absentia on Monday.
The Italian court also sentenced five co-accused.
Krekar, whose real name is Najumuddin Ahmad Faraj, has lived in Norway since 1991. He was found guilty of leading the Rawti Shax, a network with alleged links to the Islamic State group and which is suspected of planning attacks in the West.
His Norwegian lawyer Brynjar Meling said Tuesday that his client rejected the charge and added that "all appeal avenues" would be pursued.
"He has no connection with IS," Meling told AFP after the Italian court ruling.
"His only goal is to come back to Kurdistan in Iraq and be able to (be a) politician there, set up a political party he wants to establish in Iraq as a free man," Meling said.
Considered a threat to national security and featuring on UN and US terror lists, Krekar has been at risk of deportation since 2003.
Norwegian law, however, bars his deportation to Iraq because he risks the death penalty there.
Italy in 2016 cancelled a request for Krekar's extradition, disappointing Norwegian officials who saw a lost chance to be relieved of the mullah they saw as troublesome.
He had spent several years in jail in Norway for threats and inciting violence.