The interior ministry on Friday also defended the presence of thousands of riot police who chased and beat activists during protests.
The violence broke out when protesters tried to gather in support of two judges due to appear on Thursday at a disciplinary hearing after they alleged fraud during parliament elections last year.
The ministry put out a statement saying police forces were deployed outside a Cairo court where the hearing was to be held to "protect this important judicial institution".
The ministry said the police presence was necessary because people had "gathered and protested without obtaining a permit".
Accusations of fraud
The two judges, Hisham el-Bastiwisy and Mahmoud Mekki, became heroes of the democracy movement after they went public with allegations of fraud during parliamentary elections last year.
According to the statement, the prosecution was interrogating "elements who mostly belonged to illegal entities and who have insisted on gathering and obstructing traffic in the downtown area", an apparent reference to members of the banned Muslim Brotherhood who were among those arrested.
The statement did not provide figures for the arrests.
A prosecution official on Friday ordered that 255 people arrested during the protest be detained for 15 days for questioning, a judicial source said on condition of anonymity because he was not authorised to give statements to the media.
The director of the Brotherhood's website, Abdel Gelil el-Sharnoubi, said on Friday that up to 300 Brotherhood members were detained across the country on Thursday in connection with their support for the judges.
Mohammed Taima of the pro-reform Kifaya movement said about 60 Kifaya members across Egypt were arrested on Thursday. About 10 of them were later released, he added
The US State Department said it was "deeply concerned" about the police assault on protesters and would be raising the matter with the government.
"We urge the Egyptian government to permit peaceful demonstrations on behalf of reform and civil liberties," spokesman Sean McCormack told reporters.
US report questions aid
Also on Friday, a congressional report raised questions about the value of US military aid to Egypt, fueling a debate about assistance.
The Government Accountability Office (GAO) report came at a time when the administration and some lawmakers have expressed growing displeasure over Cairo's democratic backsliding and raised the prospect of aid cuts.
Congress's watchdog agency did not touch on human rights considerations but said there was no way of assessing whether the military funding was being used effectively.
Egypt, a leading recipient of US economic and military aid, has received more than $60 billion since 1979, including $34 billion in foreign military financing (FMF) credits.
But the GAO said, "Although officials and several experts assert that the FMF program to Egypt supports US foreign policy and security goals, State and DOD (Department of Defense) do not assess how the program specifically contributes to these goals."
The GAO recommended that the secretaries of state and defense study possible changes in future grants and review the programme.