Egypt's Muslim Brotherhood is calling for protests to denounce the military's toppling of President Mohammed Morsi, while opponents of the ousted Islamist leader also are urging supporters to take to the streets for mass rallies.

The calls for competing rallies have renewed fears of street violence, two days after clashes between the rival camps left at least 36 people dead and more than 1,000 wounded.

The Brotherhood, which helped propel Mr Morsi to power as Egypt's first democratically elected leader, has denounced the military takeover as a "coup," and is demanding he be reinstated.

The collection of liberal, secular and youth groups that spearheaded the campaign to oust Mr Morsi, meanwhile, have called for a mass rally in Cairo's Tahrir Square to support the country's new interim government.