Now, through their election sweep in January, the Shiite groups control the government.
The police said that two members of the Shiite group had been killed and seven wounded.
In addition, the group does not have a big following among Shiite groups based in Iraq.
Until last week, the Shiite groups had mostly sat out the resistance.
The streets are awash with talk that the men were killed by conservative Shiite groups.
The two Shiite groups have frequently clashed in the past.
These men answer only to a self-appointed provincial council of Shiite religious groups, which wants no one else to deal with the British.
Sunni political parties, as well as some Shiite groups, strongly oppose the wall.
Iran will also need a working relationship with Iraqi Shiite groups, who stand to gain a degree of political power.
Whether the Shiite groups will be more conciliatory on other issues remains to be seen.