Two people in Qalyoub had been killed by gunfire and the third was hit by a train while fleeing the violence.
At least a further 27 people have been injured in the clashes, three critically, in the worst violence in the Egyptian capital since July 16, when seven died in confrontations.
Injured people have been removed from the fighting and seven Morsi supporters have been detained, according to state media.
An Egyptian security official says supporters of Egypt's ousted President Mohamed Morsi are clashing with opponents holding a sit-in in Cairo's Tahrir Square.
Al Jazeera's Nicole Johnston, reporting from Cairo, said that at this stage it was impossible to verify how the fighting began.
"It certainly started off peacefully, and then the anti-Morsi crowd met the pro-Morsi crowd and the fighting began," our correspondent said.
"It has been reported that people on both sides have guns. Normally we do not see violence so early in the day and the police intervened very quickly, firing teargas in an attempt to disperse the crowd.
"At this stage that does not seem to have worked."
The violence started when several hundred pro-Morsi protesters were marching towards the US Embassy to hold a demonstration against alleged American meddling in Egypt's affairs, the official said.
The march passed an entrance to Tahrir Square manned by anti-Morsi protesters, and the two sides pelted each other with rocks. Gunfire was heard, but it was not clear who was firing.
Armored vehicles moved and blocked the road, the official said, speaking on condition of anonymity because he was not authorised to speak to the press.
The Muslim Brotherhood has staged daily protests across the country since Morsi was deposed on July 3, demanding his reinstatement.
Al Jazeera and wire services