CAIRO, July 3 (Reuters) - Organisers of the protest movement that drew millions of Egyptians on to the streets this week to demand the resignation of Islamist President Mohamed Mursi called on his military guard on Wednesday to arrest him.

Dismissing the claims to legitimacy that Mursi made in a televised address, the "Tamarud - Rebel!" movement said in a statement: "The only response to Mursi's speech is to protest on the streets in our millions, starting on Wednesday, so that he and his group hear the voice of the great Egyptian people.

"Not only are we calling for his departure but we call for him and his group to be sent for trial. We call on the Republican Guard to arrest Mohamed Mursi and send him for trial immediately."

Mursi and his Muslim Brotherhood have rejected an armed forces ultimatum for him to share power with the opposition by Wednesday afternoon or face a solution imposed by the military. (Reporting by Yasmine Saleh; Editing by Alastair Macdonald)