Police fired live bullets to break up the rallies in some parts of the Democratic Republic of Congo's capital, witnesses said yesterday.
Officers also used tear gas to disperse groups of rock-hurling youths as tyres burned at several main intersections and a police helicopter buzzed overhead.
"Two policemen were killed by bullets," government spokesman Lambert Mende said, adding that "two looters" had also died.
Around 10 demonstrators were admitted to hospital with gunshot wounds, according to hospital sources.
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Shots rang out from several places, including near the University of Kinshasa after police warned they would open fire if protesting students failed to leave, an AFP correspondent saw.
Demonstrators called for Kabila "to leave at the end of his term", while some carried signs saying: "Don't touch the constitution".
Several cars were torched and witnesses said some looting had occurred on the fringes of the clashes.
Burkina Faso's president Blaise Compaore was chased from power in October when he tried to change the constitution.
Before Compaore it was Senegal's octogenarian Abdoulaye Wade whose bid for a controversial third term sparked deadly protests in Dakar. However, proving they would not stand for it, the Senegalese roundly voted in his arch-rival Macky Sall.
Chad, Cameroon, Gabon and Togo all now allow their leaders to keep running for office as long as they like.
Streets were deserted in several parts of Kinshasa yesterday with public transport interrupted and many children kept home from school.
From 8:00 am (local time), police and elite troops of the Republican Guard sealed off the parliament building, where the lower house passed the controversial bill on Saturday.