After Harith al-Obeidi was shot at a Baghdad mosque, President Jalal Talabani called for national unity 'in the face of powers that seek to provoke strife and destabilize the country.'
The deal would be part of a reconciliation effort between Iraq's government and extremist Shiite groups.
The Haqqani network, born of the Russian war and nurtured by the CIA, is behind many spectacular assaults in Afghanistan.
US intelligence officials do not see a reversal in security gains, but Iraqi political maneuvering could affect decisions to keep US troops in trouble spots.
The man he wants for the post, Lt. Gen. Stanley McChrystal, is deeply versed in special operations.
Iraqi security forces say they arrested Abu Omar al-Baghdadi in April. US officials say they are uncertain whether the name refers to a specific person or is simply a commonly used pseudonym within the insurgency.
The recent spate of attacks have come as US troops are preparing to pull out of urban areas.
Al Qaeda in Iraq appears to be exploiting instability in Iraq's government
The arrest is perhaps the greatest blow to the insurgency since Zarqawi was killed in 2006.