The Muslim Brotherhood has called for mass protests in response to the military coup that led to the fall of former President Mohamed Morsi.
An Islamist coalition, led by the Brotherhood, urged people on Thursday to take part in a "Friday of Rejection" protest following weekly prayers.
The call is being seen as a test of whether Morsi still has a support base in the country, and how the army will deal with it.
Egypt's army released a statement later on Thursday on its Facebook page, saying that everyone had a right to peaceful protest, but that right should not be abused.
Excessive protests, the army warned, could lead to civil unrest, while re-iterating that it was not targeting any political group.
"Wisdom, true nationalism and constructive human values that all religions have called for, require us now to avoid taking any exceptional or arbitrary measures against any faction or political current," the statement said.
"Peaceful protest and freedom of expression are rights guaranteed to everyone, which Egyptians have earned as one of the most important gains of their glorious revolution," according to the army's statement.
"Excessive use of this right without reason could carry some negative implications, including blocking roads, delaying public benefits and destroying institutions, posing a threat to social peace, the national interest and damaging the security and economy in our precious Egypt."
Newly sworn-in interim leader Adly Mansour used his inauguration as an apparent attempt to heal the relationship with the Brotherhood.
"The Muslim Brotherhood are part of this people and are invited to participate in building the nation as nobody will be excluded, and if they respond to the invitation, they will be welcomed," he said.
Egypt's army had rounded up the leadership of the Muslim Brotherhood as a top judge took oath of office as the country's interim leader, a day after the military chief toppled President Mohamed Morsi from power.
The army turned the screws on the Brotherhood on Thursday, with military police arresting the group's supreme leader Mohamed Badie "for inciting the killing of protesters", as Brotherhood supporters protested the abrupt end of Morsi's one year rule.
He, and his powerful deputy, Khairat el-Shater, were wanted for questioning on their role in the killing this week of eight demonstrators in clashes outside the Brotherhood's Cairo headquarters.
The military chief General Abdel Fattah al-Sisi on Wednesday announced the removal of Morsi after days of nationwide protests by opposition groups calling for the Islamist president's ouster.
A judicial source said the prosecution would on Monday begin questioning members of the group, including Morsi, for "insulting the judiciary" as the charges begin to pile up.
Other Brotherhood leaders would be questioned on the same charges, including the head of the group's political arm Saad al-Katatni, Mohammed al-Beltagui, Gamal Gibril and Taher Abdel Mohsen.
Morsi and other senior leaders have also been banned from travel pending investigation into their involvement in a prison break in 2011.
The deposed president himself has been held in an unknown location since the generals pushed him out.