Four people were killed and two wounded on Monday after an explosion destroyed their armoured civilian vehicle just outside the sprawling complex housing the US-led occupation administration.
Two of those killed in the blast were British civilians, according to the British Foreign Office.
And another three people, including a child, were killed in an explosion that destroyed their car only minutes before a US convoy drove by, witnesses said.
The first suspected resistance attack occurred about 50m from the Assassins Gate, one of the main entrances to the so-called Green Zone, at around 2:00pm (11:00 GMT).
Latest reports say a rocket-propelled grenade destroyed the vehicle.
Sadr City clashes
Meanwhile, US troops - who have vowed to wipe out Shia leader Muqtada al-Sadr's private army - clashed with the militia overnight in a district of Baghdad where he has strong support.
The Green Zone is a frequent
target of resistance attacks
Hospital officials said 18 civilians were killed in the populous Sadr City area. But the occupation authority put the figure at 26 and said all were militiamen loyal to al-Sadr.
The US military said its soldiers had already killed "an estimated 21" militiamen over the weekend after coming under small arms and rocket-propelled grenade fire in Sadr City.
Al-Sadr's Mahdi Army has been involved in weeks of clashes with the occupation forces, mainly in central Iraq, after the US-led authorities closed down his newspaper and threatened to arrest him.
Series of assaults
The Baghdad bomb attacks are the latest in a series of deadly assaults in the Iraqi capital.
On Saturday, a car bomber in Baghdad killed four people and slightly wounded a deputy interior minister in Baghdad.
On 17 May, the president of the Iraqi Governing Council, Izz al-Din Salim, was killed along with at least six other people near the occupation headquarters.
In the country's north, four cinemas in Mosul were shaken by loud blasts on Monday, but police said minimal amounts of explosives were used and there had been no damage or casualties.
An Iraqi police source told Aljazeera that unknown men launched the attacks probably due to the showing of "immoral" films.