Their investigation continued as military commanders said troops would not be forced to remain inside their base.
The dead soldiers, who were all in their 30s, have been named as Major Matthew Titchener, Warrant Officer Colin Wall and Corporal Dewi Pritchard.
In a statement on Sunday night the family of Cpl Pritchard paid tribute to his bravery, but also raised concerns about the safety of soldiers in Iraq.
They said: "There remains at this early stage many unanswered questions concerning personal protection and security arrangements for British troops in Basra."
'Moving everything
As tributes were paid to the three men, whose bodies are due to be flown home within the next three days, their commander said the killers would be found.
Brigadier Brian Moore, head of the 19 Mechanised Brigade, said "one or two" people had been detained for questioning.
He said: "We are moving everything that we have to find the people who killed our three colleagues and bring them to justice."
Brigadier Moore said that on Saturday part of Basra had been closed off and during the night a number of operations took place to follow up on intelligence leads.
The troops had been driving away from their base on a routine patrol when, according to witnesses, gunmen in a red pick-up truck opened fire and threw a grenade at them.
'Beloved wife'
The family of 35-year-old Corporal Pritchard paid tribute to him as "brave, professional and proud".
They said: "His tragic death in Basra robs his beloved wife Tracey of a husband and his children Kira and Ethan of a father."
Dewi had only returned to Basra last Friday having been home on leave for six days, the family added.
Major Titchener, 32, from Southport in Merseyside, was married with one child.
Warrant Officer Wall, 34, from County Durham, was married with one child, and had two children from a previous marriage.
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