Shots could be heard in Kinshasa and several other towns on Saturday as Tshisekedi clashed with security forces.
Six people had been killed by Saturday afternoon, according to the UN's Radio Okapi.
Earlier the main rival of Laurent Kabila rejected the election commission’s declaration that the incumbent had been reelected.
Police said Saturday that they were controlling the situation.
Government officials lashed out at Tshisekedi, calling his declaration “a breach of the law, an attack on the constitution”.
A heavy security forces presence was on the streets on Saturday, with 20,000 soldiers on standby.
Some residents accused police of robbing them.
Clashes were reported in the Tshisekedi stronghold of Kananga on Friday, with at least one person killed.
UN Secretary-General Ban Ki-moon appealed for calm.
The official results "indicated" Kabila has won, said his spokesperson Martin Nesirky in a statement released late Friday.
It called for “any differences regarding the provisional results of the polls to be resolved peacefully through available legal and mediation mechanisms".