Talabani, who was also recently re-appointed, delayed naming a premier to give Maliki, as incumbent, more time to negotiate ministerial positions with rival blocs in parliament.
But he has another 30 days before he is obliged to announce his cabinet.
After an election which saw former prime minister Iyad Allawi’s Iraqiya coalition win the most seats, the government will be chosen according a points system based on its support at the polls.
The rival blocs have all formed committees to bargain for places.
Maliki appealed to them to name candidates who have “experience, loyalty and integrity” and promised “a government of partnership [in which] no one will be neglected”.
Iraqiya, which campaigned as a non-sectarian alliance involving both Shia and Sunni-Muslims, won most of its seats in Sunni areas. Its support is considered vital to reduce the chances of a revival of inter-confessional violence.
A power-sharing pact was agreed on 10 November but has proved fragile. Iraqiya members walked out of a parliamentary session the day after it was made, demanding that three of their MPs be reinstated after being barred for their alleged ties to Saddam Hussein’s Ba’ath party.