Bombs killed 25 people in Baghdad, while sectarian attacks wrecked six Shi'ite shrines in a rural area, adding to pressure on Mr Maliki, who has a week to meet a constitutional deadline to present a broad-based coalition government.
Fourteen Iraqis were killed and six wounded in two suicide car bombings at the checkpoint leading to the Baghdad International Airport.
Two vehicles packed with explosives were detonated in a parking lot near the checkpoint, the US military said in a statement. Three other bombs killed 11 people around the city.
In the north between Kirkuk and Tikrit, a convoy of Foreign Minister Hoshyar Zebari's bodyguards was hit by a bomb killing three, though the Kurdish politician was not travelling in the motorcade.
Clashes between insurgents and police as well as a suicide car bomb claimed the lives of a policemen and two civilians in the northern city of Mosul.
Eight people were killed and six were wounded in and around the restive city of Baquba, where three kidnappings also took place, police said.
Insurgents destroyed at least two small shrines of local Shi'ite holy figures, the Abdullah bin Ali shrine in the village of Wajhiya and the Tamim shrine, both in mixed Sunni-Shiite areas.
Meanwhile, two British soldiers were killed on Saturday and one other wounded after a roadside bomb exploded in the southern Iraqi city of Basra, the Ministry of Defence said.
Their deaths bring to 111 the number of British troop fatalities in Iraq since the March 2003 US-led invasion.
New cabinet closer
The violence came as Mr Maliki appeared set to break weeks of deadlock over the new government by leaving the controversial interior and defence portfolios vacant, instead keeping them in his own hands for the time being.
"I think prime minister Nuri al-Maliki will announce the government without interior and defence," Bahaa al-Aaraji, an MP close to Shi'ite radical leader Moqtada al-Sadr, told reporters.
"He will be the acting minister of interior and defence and then, maybe after two or three weeks, he will appoint the appropriate people for these jobs," he said.
An MP from Mr Maliki's own Dawa party, Hassan al-Seniad, had already raised the possibility of the premier designate keeping some portfolios in his own hands as he bids to finalise a cabinet line-up in the next 48 hours.
But the manner in which the new premier has conducted the talks drew an angry response from one of the smaller factions in his Shi'ite United Iraqi Alliance, which announced that it was abandoning the list on which it fought December's parliamentary elections.
"Our decision is final," said Sabah al-Saadi, spokesman for the Fadhila party, which holds 15 of the alliance's 128 seats in the 275-seat parliament. "Even if they give us the oil ministry now, we will not rejoin the negotiations," he said.
The party held the oil ministry in the outgoing government, but reports suggested the portfolio was likely to go to Shi'ite independent Hussein Shahristani in the new line-up.
Fadhila's walkout was matched by threats to quit the talks from the main Sunni Arab bloc, whose participation in a national unity government is seen as vital if the sting is to be taken out of the insurgency raging in Sunni areas.
"If we don't get our rights, we will review our participation in the entire political process," warned Salman al-Jumayli, an MP with the National Concord Front.
"We are still negotiating to form the government and are asking for the ministries of education, health and planning.
The Sunnis would also like to retain the defence ministry, especially if the interior ministry remains with one of the main
Shi'ite parties.