The founder of Christians Against the Coup has been arrested at Cairo airport while attempting to fly to Qatar, the Freedom and Justice news website reported.
Ramy Jan, a Coptic Christian, is an outspoken supporter of ousted Islamist president Mohamed Morsi.
During Morsi's presidency, Jan defended the Muslim Brotherhood and its Freedom and Justice Party. He encouraged Christians to join the party, which he said was not sectarian.
Coptic Orthodox Pope Tawadros II, together with Al-Azhar Grand Imam Ahmed El-Tayeb, were present alongside army chief Abdel-Fattah El-Sisi when he announced Morsi's ouster on 3 July 2013.
Churches were attacked and torched in several parts of Egypt after security forces dispersed pro-Morsi sit-ins in August 2013. Morsi supporters have often blamed Christians for the mass demonstrations that led to the ouster of the Islamist president.
There are no official statistics showing the number of Christians in Egypt. The Coptic Church estimates the community at 15 to 18 million. While the state's Central Agency for Public Mobilization and Statistics (CAPMAS) estimated in 2012 their number to be around 5.1 million.