Lawyers for the Muslim Brotherhood have submitted a complaint to the ICC asking it to investigate the military's alleged crimes against humanity in Egypt, they said in London on Monday.
Lawyers acting for the Brotherhood's Freedom and Justice Party said they hoped to meet with the International Criminal Court prosecutor in the coming months to discuss opening a preliminary investigation.
The lawyers told a press conference they had submitted a declaration on behalf of ousted Islamist president Mohamed Morsi accepting the ICC's jurisdiction in Egypt even though it is not a signatory, and he is no longer in power.
They have also submitted a complaint detailing alleged evidence of crimes since Morsi and his Brotherhood were ousted by the military on July 3 last year.
"The message must be sent out clearly to the Egyptian military regime that it runs the risk of prosecution. This is what the declaration accepting the jurisdiction aims to achieve," said lawyer John Dugard.
More than 1,000 people have been killed in street clashes and thousands imprisoned in a police crackdown on the Muslim Brotherhood since Morsi was ousted.
The military-installed government last month declared the movement a terrorist organisation.
The London legal team is led by Tayab Ali of human rights law firm ITN Solicitors. He said their funding came from alleged Egyptian victims of the military.
Egypt is not party to the ICC and Morsi is not in office so it is unclear how far the complaint can go. However, the legal team takes the view that Morsi's administration remains the lawful, democratically-elected government of Egypt.
They have submitted a declaration, in Morsi's name, accepting ICC jurisdiction over Egypt in respect of crimes against humanity committed since the coup.
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The court in The Hague says that non-signatory states can accept its jurisdiction with respect to crimes committed in its territory or by one of its nationals, and request an investigation by the ICC prosecutor.
The prosecutor can also bring forward cases based on an assessment of the evidence.
"We hope and have good reason to believe the court will take this declaration seriously," said Dugard, a former United Nations human rights special rapporteur.
"The only question is who may make a declaration accepting the jurisdiction of the ICC.
"The main purpose of this exercise is to ensure that those who have committed international crimes will not go unpunished.
"Hopefully this will deter them from future misdoings."
The second part, the complaint, submitted to the ICC on December 20, includes alleged evidence of murder, unlawful imprisonment, torture, persecution against an identifiable group and enforced disappearance of persons.
It also includes claims of bulldozers running demonstrators over and targeted shootings.
On August 14, at least 627 people were killed when security forces stormed Cairo's Rabaa al-Adawiya Square to disperse a sit-in by Morsi's backers. It was the deadliest mass killing in Egypt's modern history.
The complaint names individual suspects in the Egyptian military, but the lawyers did not wish to divulge them publicly.
The ICC says national judicial systems retain their responsibility for trying perpetrators of crimes, but the lawyers claimed there was no sign of this happening in Cairo.
"Whatever happens in the future of Egypt, these crimes cannot be swept under the carpet. They're going to have to be investigated, and the ICC is in a position to do that right now," said lawyer Rodney Dixon.