Maliki, a Shiite, has had a troubled relationship with Iraq's Sunni tribes, who in 2006 began helping the government fight Al-Qaeda-linked Sunni militants, but who now accuse him of sectarian discrimination.
The Iraqi premier's fresh overtures to tribal chiefs comes amid an onslaught spearheaded by Islamic State Sunni militants that has taken swathes of the country in recent weeks.
"He stressed that the tribe was and still is the foundation for protecting the security of areas against the dangers that threaten them, particularly terrorists," a statement from Maliki's office said.
From late 2006, when Iraq's bloody sectarian war was around its peak, some Sunni tribes began siding with US forces against the often brutal tactics of their Al-Qaeda-linked co-religionists.
Also Read
The American military started paying the militiamen regular salaries, and called them the "Sons of Iraq". In Arabic, they were referred to as the Sahwa, or "Awakening", forces, and numbered around 100,000 at their peak.
The move was seen as crucial to the decline of violence in Iraq from 2008 onwards and helped provide jobs for the country's Sunni minority, dampening resentment against the Shiite-led government.
Maliki's office said he had met tribal chiefs from Sunni strongholds in the Anbar, Salaheddin, Nineveh and Kirkuk provinces, and that they had asked for a "bigger role in countering the terrorists, and for help with weapons and training."
Maliki agreed to form committees to meet their requests, his office said.