CAIRO — Amnesty International took Egypt’s new president to task on Tuesday for failing to address the ‘‘bloody legacy’’ of abuses by security forces committed under military rule after the fall of Hosni Mubarak, abuses that continue even after the establishment of the country’s first freely elected government.

The group urged President Mohammed Morsi to hold the military accountable for the killing, torture, and sexual abuse of protesters during the 18 months when the generals held power after Mubarak’s February 2011 ouster.

It also said Morsi should rein in police forces, which it said still use excessive force to deal with protests and have tortured detainees. It called for the government to allow United Nations experts to investigate and assess how to deal with the problems.

“Unless there is a clear political will to confront this and to provide the families of the victims with truth and justice, things are not going to change,’’ said Hassiba Hadj Sahraoui, deputy director for Amnesty’s Middle East and North Africa Program.

‘‘For the moment, police officers, soldiers, are confident that they can commit violations with impunity without ever having to answer for any of their acts,’’ she said.

Two extensive reports released by the London-based human rights group in Cairo on Tuesday detailed cases of rights abuses by the army and police, focusing on six separate incidents of crackdowns on protests that killed at least 120 people. Amnesty said thousands of protesters were injured or maimed during the crackdowns.