The human rights group said on Tuesday Britain was undermining the rule of law in Iraq by failing to investigate properly the suspected unlawful killings.
In a report released amid a storm of allegations about the mistreatment of Iraqi prisoners by US and UK forces, Amnesty said the British troops' actions had breached international human rights standards.
"The British Army's response to suspected unlawful killing of civilians has undermined, rather than upheld, the rule of law," it said.
"It has failed to conduct investigations into all killings of civilians, and the investigations that have been carried out have failed to ensure that justice was done and seen to be done in the eyes of the victims' families."
Amnesty said in total, UK troops had been involved in the killings of at least 37 civilians since 1 May 2003, when the war to topple Saddam Hussein officially ended.
It highlighted nine cases in the southern Iraqi areas of Basra and Amara, including those of an eight-year-old girl, Hanan Salah Matrud, shot dead on 21 August 2003 near her village.
"The British Army's response to suspected unlawful killing of civilians has undermined, rather than upheld, the rule of law"
A witness told Amnesty Hanan was killed when a soldier aimed at her and fired a shot from around 60 metres away, but the army said she was killed accidentally by a warning shot.
Amnesty also reported the death of Ghanim Kadhim Qati, who was shot outside his home while celebrating a family wedding.
It said investigations into the killings, if conducted at all, were shrouded in secrecy and victims' families had not been given adequate information about how to apply for compensation.
A Defence Ministry spokesman said the government was studying the report.
Amnesty also reported on the killings of several civilians during demonstrations and killings of supporters of Saddam Hussein's government, carried out by armed vigilante groups.
"All governments are under a duty to take action to secure right to life," Amnesty said. "In the case of suspected killings, a government must launch a thorough, competent, independent and impartial investigation ... and bring to justice persons who are reasonably suspected of responsibility."
Iraqi children have been killed by
UK troops the report says
Lawyers acting for 12 Iraqi families who allege their relatives were unlawfully killed by British troops in postwar Iraq, took their case to Britain's High Court last week.
The lawyers argue the killings were a violation of the victims' right to life under European law.
The High Court challenge and the Amnesty report will pile yet more pressure on Prime Minister Tony Blair's government, already under fierce fire about how British troops are treating Iraqi prisoners and civilians.
Thirteen months after the fall of Saddam Hussein, the administrations of both Blair and US President George Bush have been rocked by a scandal that hit the headlines, when graphic images were splashed across their national media of Iraqi prisoners being humiliated and mistreated.
Britain's Daily Mirror newspaper last week printed photographs apparently showing troops urinating on a prisoner and beating him. The authenticity of the pictures has been questioned, but the paper has since published evidence from a soldier who said he had witnessed savage beatings of Iraqis.
More damage has been wrought by the revelation that the International Committee of the Red Cross had alerted the government with a report months ago on mistreatment of Iraqi captives.
That report - leaked and published by an American newspaper - described British troops forcing Iraqi prisoners to kneel and stomping on their necks in an incident in which one captive died.
It also said US troops kept Iraqi detainees naked for days in total darkness.