Egyptian police used tear gas and water canon against protesters marking the second anniversary of the overthrow of Hosni Mubarak on Monday night.
Hundreds demonstrated against current President Mohammed Morsi who they accuse of failing to fulfil the 2011 protests' demands for democracy and social justice.
Masked men briefly blocked trains at a central Cairo underground station earlier in the day and a dozen others stopped traffic on a main road with burning tyres.
Secular groups formed the backbone of the 18-day uprising that ousted Mr Mubarak in early 2011 but they have increasingly come into conflict with Mr Morsi's Muslim Brotherhood.
State news agency Mena said 21 people were arrested at the presidential palace in Cairo, where protesters tried to break through police lines to storm the building.
Another 18 people were arrested in nearby Tanta during clashes outside government buildings.
Protesters also rallied at Tahrir Square, the epicentre of the original protests, and outside the Cairo offices of the prosecutors' office.
Opposition groups are calling security forces to be held accountable for the deaths of more than 70 protesters in recent clashes.
Although the protests were relatively small they come as recent polls showed that Mr Morsi's popularity has plummeted.
After seven months in office, only 39 per cent said they would vote for the president in new elections, down from 50 per cent a month before.
nHundreds of police officers protested across Egypt today saying they should not be used as a tool for political repression.
Some held signs saying: "We are innocent of the blood of the martyrs."
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