Separate bombings in Baghdad also claimed at least five victims
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Gunmen wearing camouflage uniforms have seized 14 people from a computer store in Baghdad, Iraqi officials say.
They drove off in what appeared to be vehicles issued by the government to security forces.
Dozens of bodies have been found in Baghdad since Sunday, and a senior intelligence official was shot dead.
The Iraqi government has announced a series of security initiatives in an attempt to reduce such attacks, which have become a frequent occurrence.
Thousands of extra US troops have been sent into Baghdad and there are plans to build a ring of trenches around the city.
Monday's mass kidnap comes a day after 26 workers were reported to have been abducted from a food processing factory in Baghdad.
Unmarked car
It was not immediately clear who was responsible for the kidnapping in Baghdad, or whether their motive was sectarian or criminal.
Correspondents say similar mass kidnappings have previously been blamed on Shia Muslim death squads and Sunni extremists, who separate their captives on sectarian lines and kill members of the opposite sect.
The intelligence officer who was shot dead, Col Faris Khalil, was driving along a main road in eastern Baghdad when gunmen drove up beside him and opened fire.
He was wearing civilian clothes and travelling in an unmarked car, an interior ministry official said.
Meanwhile, police said more than 50 bodies had been found in the Iraqi capital in the past day. All the victims had been shot and a number showed signs of torture.
South of Baghdad, seven headless torsos were recovered from the Tigris at Suwayra.
In other violence, separate bombings in central and northern Baghdad killed at least five people and wounded 10.