One of the attacks occurred before midday when gunmen stormed a jewelry store in al-Shaab district in northern Baghdad, killing two jewelers inside, the source told Xinhua on condition of anonymity.
The attackers robbed unknown amount of jewels and cash and fled the scene, the source said.
Afterwards, the attackers also traded fire with security forces in the vicinity, killing up to four policemen and two passers-by, the source said.
Ten people, including four security members, were wounded during the clash, the source added.
Despite the presence of Iraqi security forces in the area, the robbers escaped the scene in a waiting car, he said, adding that reinforcement troops from the Iraqi security forces rushed to the area and immediately started a probe into the heist.
Earlier, the source put the toll at a total of six killed and 10 wounded by the attack.
In addition, Lieutenant General Hassan al-Baidhani, spokesman of Baghdad Operations Command, responsible for security of the capital, confirmed in a statement by his office that a total of eight were killed by the attack, adding that his troops also killed one of the attackers and captured another.
"Iraqi security forces killed one of the gunmen and captured another from the group which attacked the jewelry store in northern Baghdad, and the security forces obtained photos for the attackers who were filmed on a security CCTV camera," the statement quoted Baidhani as saying.
In an earlier incident in the day, an Interior Ministry source told Xinhua that up to five policemen were killed and another injured when gunmen in a car threw a hand grenade and opened fire on the guards of the municipality of the town of Tarmiyah, some 30 km north of Baghdad.
The source earlier put the toll at four policemen were killed and two others wounded, but later in the day one of the injured was announced dead.
In the day before, Tarmiyah was the scene of another deadly attack when gunmen broke into the house of a bodyguard of the mayor of the town and shot him dead with his wife, sister and two daughters.
The attackers then planted bombs into the house and blew them up before they fled the scene.
Iraqi cities have been plagued by deadly attacks, including suicide bombings, as the country is preparing to host the Arab League summit slated for March 29.
Baghdad said it has completed its preparation for the summit and is ready to receive the Arab leaders. But recent violence across the country is seen as a setback to the Iraqi efforts to restore normalcy ahead of the summit.
Iraq sees the summit as a significant milestone in its history that would lead the country to play a powerful and positive role in the Arab world.
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