How the struggle plays out could have repercussions across the Middle East and North Africa, regions already wracked by upheaval. In nearby Gaza and Israel, tensions remain high after last month's fighting. In Syria, a civil war has raged since March 2011.
Wednesday's violence followed clashes Tuesday outside the palace, which has become the focus of protests by Egypt's liberal opposition.
On Tuesday night, police fired tear gas after anti-Morsy protesters broke through barbed wire around the palace and hurled chairs and rocks at retreating officers. After the initial clashes, police withdrew behind fences and the demonstration was peaceful for several hours.
Yassir Ali, a spokesman for the presidential office and the vice president, told reporters Wednesday that the presidential office had ordered the security forces at the palace "to protect the protesters and keep them safe."
"The orders to the security forces were not to confront (them), (but) to preserve the lives of the protesters and to prevent any clashes between the security forces and the protesters," Ali said.