Twenty eight people have been killed since Monday in anti-government protests, according to a local human rights organisation. The authorities put the death toll at five.
Protesters oppose a draft law that would enable President Joseph Kabila to extend his stay in power beyond his current mandate which ends in 2016.
Two shots rang out as dozens of students shouting "Kabila get out!" faced off against a small group of police officers. In the Ndjili neighbourhood, youths destroyed a police vehicle.
On Tuesday, hundreds of youths torched a town hall in Ngaba, a southern neighbourhood of Kinshasa, while several prisoners escaped from a neighbouring building. Looters also made off with police guns stored at the site.
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The army and police arrested at least 20 people as protesters hurled rocks at state buildings, public buses and even passing cars. Soldiers fired in the air to scare off looters who targeted a Chinese-owned store.
Tshisekedi, 82, who is recovering from illness in Belgium, has been in opposition since the 1960s, previously taking on the dictator Mobutu Sese Seko as well as Kabila's father Laurent-Desire Kabila.