Human Rights Watch says at least four more people were killed during the poll - claims dismissed by the government.
It says LRA rebels killed three people in the north-east of this vast country as they went to vote.
The first official results give Mr Kabila a narrow lead.
With 15% of the votes counted, the election commission says Mr Kabila has 940,000 votes against 912,000 for his main rival, Union for Democracy and Social Progress (UDPS) leader Etienne Tshisekedi.
These results largely come from areas seen as Kabila strongholds.
Election officials also said that their website had been hacked into and false results published there.
The election was marred by widespread logistical problems, as well as the violence and voting in some areas was extended until Thursday to allow voting material to be delivered.
DR Congo is two-thirds the size of Western Europe but has hardly any road or rail links between its major cities, so the UN peacekeeping mission distributed some election equipment by helicopter.
On Wednesday, five African observers said the elections had been "successful", despite opposition calls for the polls to be annulled.
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