"Honestly, we cannot be silent over this and we cannot be silent over Arbil being a headquarters for Daash, and Baath, and Al-Qaeda and terrorist operations," Maliki said in his weekly televised address.
Daash is the former Arabic acronym for the Islamic State jihadist group, while Baath refers to the banned party of executed dictator Saddam Hussein.
"We cannot be silent over a movement that exploited the circumstances and expanded," said Maliki, infuriated by a Kurdish announcement last week that plans were being sped up to hold a referendum on self-determination.
The highly effective peshmerga fighters were in some areas the only rampart against the jihadists but Iraqi Kurdish president Massud Barzani has since vowed they would never leave again.
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The Kurdish move came days after the proclamation of a Sunni "caliphate" by the Islamic State jihadist group that spearheaded the routing of the Iraqi army in the second city of Mosul and vast swathes of Iraq.
Maliki warned the Kurds their decision to burn bridges with Baghdad would backfire.
"They (militant groups) will lose and so will their hosts, because they failed to provide an example of patriotic partnership," he said.