The investigation's results should be made public and those responsible for unlawful killings brought to justice.
The organisation also expressed concern that the Uzbekistani authorities may use the events to justify a further clampdown on dissent, leading to waves of arbitrary arrests nationwide in the name of "national security" and the "war against terror".
Amnesty International strongly condemned the reported use of excessive force against civilians and is gravely concerned at reports that hundreds of people - men, women and children - were killed when government troops opened fire on a crowd of demonstrators in the evening of 13 May.
Official reports talk about dozens of dead, mostly law enforcement officers, but according to eyewitnesses and hospital personnel in Andizhan, interviewed before all communications with Andizhan were cut off, as many as several hundred could have been killed with many more injured.
Amnesty International said:
"The vast majority of protestors gathered in the town’s main square were unarmed and peaceful. Nevertheless troops are said to have opened fire on the crowd without warning, shooting indiscriminately at men, women and children as they fled from the main square in panic.
"Human rights defenders in Uzbekistan are warning that law enforcement officers are searching Andizhan for the alleged organizers of the demonstrations, conducting house to house searches and arbitrarily detaining anyone suspected of involvement or participation in the protests.
"The demonstrators and their families are at great risk of being arrested. Torture against detainees to obtain confessions is routine in Uzbekistan. After cutting off all communications with Andizhan and blocking access to the city, the authorities can act with impunity."
Amnesty International is deeply worried that the authorities may again use excessive force in addressing civil unrest, which erupted in Kara-Suu (Korasuv), a town on the border with Kyrgyzstan, over the weekend.
The organisation is calling on the authorities to use only proportionate force.
Reports as to what triggered events in Andizhan are confusing but may have been linked to the trial of 23 local businessmen accused of "Islamic extremism".
Amnesty International is monitoring the trial because of allegations of torture against the defendants.
For the last week up to a thousand relatives and supporters of the 23 men, who deny any connection to banned Islamic groups, have held unprecedented peaceful sit-down vigils outside the court building to protest the men's innocence and denounce the torture they allegedly suffered.
In February 1999, the Uzbek authorities arrested Islamic and secular opposition supporters or sympathizers and their families, as well as members of independent Islamic congregations on the suspicion of being involved in bombings, which the authorities described as an assassination attempt on President Karimov.
Thousands of Muslims are continuing to serve long prison sentences, convicted after unfair trials for anti-state activities.
In 2004, hundreds of men and women, said to be either devout Muslims or their relatives, were arbitrarily detained following a series of explosions and attacks on police checkpoints in the capital Tashkent and the city of Bukhara, and suicide bombings against the US and Israeli embassies. Dozens of men and women were sentenced in unfair trials on charges of "terrorism".
Evidence was reportedly obtained under torture and admitted in court.
The Uzbek authorities linked the attacks to the country’s cooperation in the US-led "war on terror". Despite this the US State Department stopped aid to the country in July 2004.
In April 2004, the European Bank for Reconstruction and Development cut aid and investment because the Uzbek government failed to meet the Bank's human rights benchmarks.
The Organisation for Security and Cooperation in Europe criticised the parliamentary elections, held in December 2004, as falling significantly short of international standards for democratic elections.
Death sentences and executions continue to take place in Uzbekistan.