Egypt is on high alert ahead of the Coptic Christmas holiday following a New Year's Day church bombing that killed 21 people.
Police have cancelled leave for top officers and are tightening surveillance of airports and ports to prevent suspects from leaving the country.
Security is also to be increased at churches for Christmas - which Copts celebrate on 7 January.
The clampdown comes amid fears of new protests by Copts following overnight clashes at Cairo's St Mark's Cathedral headquarters of Coptic leader Pope Shenouda III during which 45 policemen were wounded.
The protestors pelted a minister who had come to visit the pope and heckled other government officials while other demonstrators blocked off four main streets in Cairo before police dispersed them.
Coptic Christmas will fall on Friday - the weekly Muslim day of prayer and rest - and Shenouda said he intended to say mass as usual on Christmas Eve.
21 people were killed early on New Year's Day and 79 wounded when an apparent suicide bomber detonated his payload as hundreds of worshippers were leaving midnight at Al-Qiddissin (The Saints) church in Alexandria.
A security official said on Sunday that about 20 people were detained for questioning but there was no evidence any of them was directly connected to the attack.