The small rallies appeared to be the start of an attempt by Mubarak's 3 million-member National Democratic Party to retake momentum from protesters demanding Egypt's nearly 30-year ruler step down immediately.
The army separated about 20 Mubarak supporters from about 1,000 pro-democracy protesters in Tahrir Square, but the Mediterranean city of Alexandria saw clashes erupt between several hundred protesters and government supporters early Wednesday, Al-Jazeera television footage showed.
Several thousand people outside Mustafa Mahmoud Mosque in the upper-class neighborhood of Mohandiseen waved Egyptian flags and carried a large printed banner with Mubarak's face. Many passing cars honked in apparent support.
Police officers surrounded the area and directed traffic.