A senior member of the leftist Tagammu Party has called for rallies on 6 October – the anniversary of Egypt's victory over Israel in the 1973 war - to stifle protests planned by the Muslim Brotherhood.
Amr Abdel-Rady said the party had received "confirmed information" that the Islamist group planned to "ruin the day by attacking state-owned facilities," Al-Ahram Arabic news website reported on Monday.
Several Brotherhood-aligned Facebook pages have called on supporters to protest on 6 October against the "military coup" which has resulted in a "crumbling economy, failing tourism, corrupt government, lack of security and a constitution-amending committee that doesn't represent Egyptians."
In recent days, protests have taken place on a number of university campuses, a traditional hotbed of Islamist and political activity.
At least 29 people were injured during clashes on Sunday at three university campuses between supporters and opponents of deposed president Mohamed Morsi, some armed with guns and Molotov cocktails, state media and security sources said.
Tagammu is a long-time opponent of the Brotherhood. It recently brought a lawsuit calling for the Islamist group's dissolution.
Egypt has been gripped by turmoil since the army ousted Islamist president Mohamed Morsi on 3 July amid mass protests against his rule, prompting his Brotherhood group to engage in widespread protests.
A broad security crackdown has severely weakened the Islamist group in recent weeks.