Des Browne, Britain's new defence minister, said an investigation was under way into what caused the Lynx helicopter to crash into a building near the provincial governor's office in the city.
However, a Basra police spokesman said a rocket had downed the aircraft.
Browne added that the clashes which erupted were brought under control in hours and that the Iraqi crowd involved 200 to 300 people.
"It is not an indication of the state of either the city of Basra or the provinces that we have responsibility for," he told Sky News television channel.
"Day on day, the local forces are coming into control of this area because of the training that we have been able to give them and our allies."
Saturday's clashes began when hundreds of angry youths surrounded British troops cordoning off the crash site and began pelting them with rocks and missiles, chanting "Victory for the Mahdi army".
The helicopter crashed in a
residential area of Basra
At least four Iraqis were reported to have died in the ensuing violence, officials said.
British troops are continuing to guard the crash site, while Iraqi troops and police kept a heavy presence in the city during curfew.
The Jaish al-Mahdi (al-Mahdi Army) is the militia loyal to Shia Muslim figure Muqtada al-Sadr, who has demanded an end to the US-led occupation of Iraq and is a key figure in the Islamist Shia Alliance bloc that will lead a new national government.
Jalal Talabani, the Iraqi president, has written to Tony Blair, the British prime minister, to express his condolences, describing the incident as "a vile crime".
Basra has remained largely calm in contrast to violence in other parts of Iraq, but British troops have clashed with local authorities and Shia militias in the city.