His remarks came during a meeting with visiting British Foreign Secretary William Hague, who renewed Western calls for Iraqi leaders to unite in the face of a militant onslaught that has killed more than 1,000 people and displaced more than half a million.
On the ground, Iraqi forces launched a helicopter-borne assault aimed at opening the way for militant-held Tikrit to be retaken, while the autonomous Kurdish region's president Massud Barzani further staked its claim to the disputed city of Kirkuk.
"We should proceed in two parallel tracks," Maliki told visiting British Foreign Secretary William Hague, according to a statement issued by the premier's office.
"The first one is work on the ground and military operations against terrorists and their gatherings," he said.
"The second one is following up on the political process and holding a meeting of the parliament (on time) and electing a head of parliament and a president and forming the government."
Maliki has thus far publicly focused on a military response to the two-week crisis, and his latest comments were his clearest yet regarding finding a political solution.
He added that Iraq had purchased several used Sukhoi fighter jets from Belarus and Russia.
The Iraqi leader said that while Baghdad did not request the Syrian strikes, he "welcomed" any such move against militants led by the jihadist Islamic State of Iraq and the Levant (ISIL).
The New York Times reported that predominantly Shiite Iran is flying surveillance drones over Iraq and sending military equipment to help Baghdad in its fight against the Sunni insurgents.
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