"I believe that in the next 15 days we can have a new government and present it to parliament," Maliki told state television, amid concern a four-month power vacuum has fanned insurgent violence killing at least 123 people and wounding 153 over the past week.
An optimistic Mr Maliki, whose nomination in place of outgoing Prime Minister Ibrahim Jaafari cleared the way for an end to a protracted deadlock, said agreements reached during negotiations over his own candidacy would smooth the way for cabinet appointments.
"We have prior agreements ... that makes our work easier," he said.
Representatives of Iraq's other ethnic and religious groups were quick to stake their claims to ministerial jobs in the national unity government being formed by the Shiite prime minister designate.
Prominent Kurdish MP Mahmoud Othman said he expected the Kurds to be assigned six of Iraq's 30 ministries, including the foreign affairs portfolio they hold in the outgoing government.
The main Sunni parliamentary bloc, the National Concord Front, played down the progress that had been made, saying it "was still premature to talk about ministries".
A strong participation in the government by Sunni Arabs is seen as key to lessening their impact on anti-US insurgency.
As the political bargaining picked up pace, the urgency of a new government taking control was highlighted by fresh insurgent violence that left four dead.
In one attack, gunmen shot dead a man and his 10-year-old daughter in the restive city of Baquba, northeast of Baghdad.
The latest violence follows seven car bombings and numerous shootings in Baghdad on Monday that left 20 people dead and about 100 wounded.
The defence ministry said eight people were arrested in a Baghdad mosque Tuesday on suspicion of involvement in Monday's car bombings.
"We found them inside the mosque making car bombs and they confessed their responsibility," ministry spokesman General Abdel Aziz Mohammed told AFP.
He said that rebels carried out 469 attacks in Iraq last week, of which 173 resulted in casualties.
Iraqi politicians have been under intense US pressure to form a national unity government as quickly as possible to get to grips with mounting sectarian violence and to take the sting out of the insurgency raging in Sunni Arab areas.
Warning from Rumsfeld
US Defence Secretary Donald Rumsfeld hailed the end of the protracted deadlock over the choice of prime minister as "a thrilling accomplishment."
But he warned it was reasonable to expect that insurgents would try to sabotage the formation of a new government by Mr Maliki, who by law has 30 days to present his cabinet line-up to parliament.
US concern has been compounded by one of the bloodiest months for US troops since the 2003 invasion.
About 60 US servicemen have died in April alone, taking the military's death toll since the invasion to 2,392, according to a count based on Pentagon figures.
Rumsfeld, who faces criticism at home for botching the Iraq invasion by initially sending too few troops, said he hoped the United States would be able to reduce its troop commitment after key ministries assert themselves.
"As we are able to pass over more responsibility, one would think we would be able to continue reducing down our forces," he said.
Meanwhile Syria has agreed to take a group of 181 Palestinian refugees currently stranded on the border between Iraq and Jordan.
The Palestinian refugees fled violence in the Iraqi capital, Baghdad, last month and have been camping out on the border since Jordan blocked their entry.
Jordan, which is already home to around 1.7 million Palestinians who fled Israeli violence over the years, has rejected criticism from human rights groups, saying it cannot cope with more refugees.