"We reject such provocative remarks by Maliki which are seen as a sort of threat, intimidation and hostility against part of the Iraqi people," Deputy Prime Minister Roz Nuri Shawez told a news conference in Baghdad.
"Such statements are meant to hide the (government's) security failure by blaming others, and we announce our boycott to the cabinet meetings in protest against such acts and stances," Xinhua quoted Shawez as saying.
Maliki made the controversial comments Wednesday, a move many saw as stoking sectarian and ethnic divisions in a country facing a severe Islamist insurgency amid a poorly organised military.
Maliki called on the authorities of Arbil to stop the activities of opposition
"We will never be silent that Arbil become a base of operation for Daash (Arabic first letters of the Islamic State in Iraq and Greater Syria or ISIS), Baath, Al Qaeda and other terrorists," Maliki said in his speech.
Maliki called on the authorities of Arbil, the capital of the semi-autonomous region of Kurdistan, to stop the activities of opposition politicians and political figures of Sunni insurgent groups.
For years, the Shia Iraqi prime minister has been at odds with the Kurds, and relations between the central government in Baghdad and authorities in Kurdistan further deteriorated after the Sunni insurgents took control of several provinces adjacent to the Kurdish region.
Earlier, regional leader Masoud Barzani said the Kurdish security forces, known as Peshmerga, took over disputed areas in the north after the Iraqi security forces fled abandoning their positions just as the insurgency escalated.
The disputed areas are ethnically mixed with Kurds, Arabs and Turkmans, as well as other ethnicities.
The Kurds have made claims on various disputed areas in northern Iraq, including the oil-rich province of Kirkuk and other areas such as Nineveh, Salahudin and Diyala.