In the first attack, a suicide bomber wearing an explosive belt blew himself up inside a minibus full of Iraqi army recruits in west Baghdad, killing at least 16 and wounding seven.
The bomber had boarded the bus outside al-Muthana recruiting centre in western Baghdad.
Recruitment centres for the Iraqi army and police, main elements of Washington's strategy for pulling out its own troops, have been frequent targets in Iraq.
A second suicide car bomber attempted to attack a US convoy in eastern Baghdad, killing at least four Iraqi bystanders and injuring three others, police said.
In overnight attacks in Baghdad and northern Iraq, gunmen killed at least nine people.
Telephone exchange attacked
In the Alawiya commercial area of central Baghdad, assailants opened fire at a telephone exchange centre early on Monday morning, killing a man and a woman.
And in clashes between gunmen and police in the al-Maalif area of southern Baghdad late on Sunday night, two policemen were killed.
The occupants of two cars ambushed a bus carrying oil employees in northern Iraq, killing four and injuring another on Sunday night.
The bus had been taking the employees from Beiji, the country's biggest refinery 250km north of Baghdad, to Tuz Khurmato district, some 120km southeast of Beiji.
A US soldier was also killed by small arms fire after his patrol came under attack north of the capital, the US military command said on Monday.
Last week, the US military handed over operational command of the Iraqi army to Nuri al-Maliki, Iraq's prime minister.