The Reform and Jihad Front, in a statement emailed to AFP, said it would call for a boycott of Norwegian goods and the international isolation of the government if Oslo went ahead with attempts to expel Krekar.
It also called on "all the good people who still fight human rights attackers to take an action and stop that bad thing".
"We (ask) all the forces of the Muslims, governments, organisations and notable persons and ask them to take an action which gets our prestige back," the statement said.
It did not specify the nature of the "action" that should be taken.
Norway's Supreme Court on November 8 upheld previous court rulings and a 2003 decision by the Norwegian authorities to expel Krekar, an Iraqi Kurd, on the grounds that he was a national security concern.
Norwegian law however prevents Krekar, whose real name is Fateh Najmeddin Faraj, from being deported to his homeland until the situation in Iraq improves.
"If this decision of the Norway government is not revised, we will call for a wide boycott of their goods and that there be no dealing with them," the statement said.
"This issue -- if not treated carefully -- will end up (really painfully) for Norway's government and they will repent of their decision," it warned.
"The Front is seriously watching developments and expresses its deep concern about these action against Sheikh Krekar who has been living there legally for a long time and never committed a crime or harmed anyone."
The Reform and Jihad Front, the most powerful insurgent group in Iraq, was launched in April last year and comprises the Islamic Army in Iraq, the Mujahedeen Army, the Fatihin Army and a rebel branch of Ansar Al-Sunna.
Krekar has lived in Norway as a refugee since 1991 and has been under threat of deportation since Norwegian media revealed he was the founder of Ansar al-Islam, which figures on the United States' list of terrorist organisations.
The Iraqi Kurd admits that he founded the group but insists he has not headed it since May 2002.
Krekar is adamant his life would be in danger if he returned to Iraq.
He has come out in support of "jihad", or holy war, in Iraq and has compared the US-led occupation of Iraq to the Nazi invasion of European countries, and insisted that Al-Qaeda chief Osama bin Laden is "a good man".Source: AFP (English)