Amnesty International urged Egypt's President Mohamed Morsi on Tuesday to implement reforms in the police and army, publishing two reports condemning human rights abuses by security forces.

Morsi "has a historic opportunity to tackle the bloody legacy of police and army and guarantee that no one is above the law in Egypt," the human rights watchdog said.

It called on him to introduce "sweeping reform" to the security forces, highlighting alleged human rights violations during the military-led transition that followed the uprising that toppled Hosni Mubarak last year.

In the reports presented to Cairo, Amnesty condemned "unlawful killings, excessive use of force, torture and other ill-treatment against protesters by both the military and the police" during the 16-month post-revolution period.

The Supreme Council of the Armed Forces (SCAF) led the country from Mubarak's ouster in February 2011 until Morsi took over as president in June 2012.

Amnesty's first report focused on several demonstrations violently suppressed by security forces.

"The military courts failed to provide any redress for the victims, while civilian investigators were unable or unwilling to indict a single officer for their crimes," it said.

"Male and female protesters were subjected to severe beatings, given electric shocks, sexually threatened and abused by military troops. Thousands were tried or face unfair trial before military courts," it added.

Morsi, who rose through the ranks of the Muslim Brotherhood before running for office, is the first civilian and democratically elected president in Egypt's history.

In August, he ordered the surprise retirement of his powerful defence minister and scrapped a constitutional document that gave sweeping powers to the military, in a move some said was aimed at ending the SCAF's power.

"The army is back in the barracks today, but the authorities should be under no illusion that they can sweep under the carpet 16 months of abuse that translated into more than 120 deaths, thousands of people being tried by military courts and hundreds tortured," Hassiba Hadj Sahraoui, Deputy Middle East and North Africa Programme Director at Amnesty told reporters.

The second report highlighted the "total impunity enjoyed" by Egypt's police forces.

"The report highlights the brutal response by the police to protests, as well as the longstanding pattern of torture of detainees and the brazen disregard of the rule of law," Amnesty said.

"The riot police have routinely responded to peaceful protests with excessive and lethal force," it said, adding that tear gas and shotgun ammunition were "among the US-made weaponry supplied to Egypt's police forces before and after the uprising."

"Since the election of Mohamed Morsi in June 2012, the security forces have continued to commit human rights violations," the report said.

"Today, torture and other abuses continue unchecked and unchallenged. From February 2011 until today there has been no significant measures to reform the police," Sahraoui said.

"Unless there is a political will in Egypt to confront a culture of abuse and rampant impunity, which translate into true reform of the police, the abuses which defined the rule of Hosni Mubarak will continue unabated," she said.