US officials responsible for the secret CIA drone campaign against suspected terrorists in Pakistan may have committed war crimes and should stand trial, a report by a leading human rights group warns. Amnesty International has highlighted the case of a grandmother who was killed while she was picking vegetables and other incidents which could have broken international laws designed to protect civilians.

The report is issued in conjunction with an investigation by Human Rights Watch detailing missile attacks in Yemen which the group believes could contravene the laws of armed conflict, international human rights law and Barack Obama's own guidelines on drones.

The reports are being published while Nawaz Sharif, Pakistan's prime minister, is in Washington. Sharif has promised to tell Obama that the drone strikes – which have caused outrage in Pakistan – must end.

Getting to the bottom of individual strikes is exceptionally difficult in the restive areas bordering Afghanistan, where thousands of militants have settled. People are often terrified of speaking out, fearing retribution from both militants and the state, which is widely suspected of colluding with the CIA-led campaign.