The first explosion missed the police patrol but struck the Sadriya market in a mixed Shia-Sunni Arab neighbourhood in central Baghdad, killing four people and wounding 27, according to police Lieutenant Ali Mitaab and Lieutenant Thaer Mahmoud.
Hours later, a parked car bomb hit a police patrol elsewhere in Baghdad, killing five people and wounding 14. The explosion targeted the patrol in Karradah, a popular shopping area in downtown Baghdad, police said.
Armed men also stopped a minivan carrying Sunni passengers on the highway from Baghdad to Abu Ghraib, ordered them off the bus and opened fire, killing four and wounding another, police Captain Jamil Hussein said.
The attacks came after Iraqi authorities imposed a four-hour driving ban on Friday in Baghdad to prevent reprisal attacks after Abu Musab al-Zarqawi's killing in a US air strike.
A similar ban remains in effect in Diyala province northeast of Baghdad, where the al-Qaida in Iraq leader was killed on Wednesday.
No troops cut
In Washington, George Bush, the president, said US and Iraqi forces will capitalise on the death of al-Zarqawi by cracking down on fighters trying to regroup after losing their leader, blamed for some of Iraq's bloodiest attacks since the US invasion in 2003.
Signalling that the US was not ready to start scaling back its military presence of 130,000 soldiers, he warned that violence may get worse in the coming weeks.
"Zarqawi is dead, but the difficult and necessary mission in Iraq continues," Bush said.
Violence shows no sign of abating
despite al-Zarqawi's killing
Also on Saturday, armed men killed a member of the Sunni Iraqi Islamic Party, Riyadh al-Naji, on the road between the towns of Latifiya and Iskandariya, south of Baghdad, police said.
And in Mosul, 390km north of Baghdad, armed men stormed neighbouring butcher shops and shot dead five butchers and wounded one, police said.
The US military said in a statement on Saturday that a US soldier was killed and another wounded when a roadside bomb struck their patrol west of Kirkuk, 250km north of Baghdad, on Friday.
Police found the severed heads of two Sunni Arab brothers in the small town of Khan Bani Saad near Baquba, 65km north of Baghdad, police sources said on Saturday. They had been kidnapped from their workplace in Baquba a week ago.
In other violent attacks, armed men ambushed and wounded three civilians in a car 25km northeast of the northern oil city of Kirkuk, police said.
A civilian in a car was killed when a roadside bomb exploded in the town of Hawija, about 60km southwest of Kirkuk, on Friday evening, police said.
Two civilians were wounded when a roadside bomb exploded near a US patrol in central Kirkuk 250, km north of Baghdad, on Friday, police said.
One Iraqi policeman was wounded when a roadside bomb exploded near his patrol in central Kirkuk on Friday night, police said.