About 25 million people are registered to vote in the run-off vote between Joseph Kabila, the incumbent, and Jean-Pierre Bemba, a former commander.
Kabila and Bemba were the top two candidates in the first-round elections held on July 30.
Kabila received 45 per cent of the votes in the first round and is expected to win the election.
The vote, part of the first democratic polls in the Democratic Republic of Congo (DRC) for 40 years, will be accompanied by provincial elections, but results are not expected for three weeks.
An end to fighting
The vote is meant to be the final step in a peace process designed to end a 1998-2003 war which was the bloodiest conflict since the second world war.
Joseph Kabila is expected to be re-elected in Sunday's elections
More than four million people died in the humanitarian catastrophe caused by the war.
More than 1,200 people still die every day mostly from hunger and disease.
Supporters of Kabila and Bemba have clashed several times since the first round of voting. In August, their private armies fought three days of battles in the capital killing more than 30 people.
They have brought in more arms and reinforcements since then.
Bemba is believed to have 600 fighters in the chaotic capital, while Kabila has at least 5,000 members of his personal guard.
Congolese police killed two people when they opened fire to disperse a riot by Bemba supporters who had destroyed a polling station when they discovered alleged ballot stuffing in favour of his rival, Yves Mobando, governor of Equateur province, said.
"Two people were killed when the police opened fire to disperse the crowds," Mobando told Reuters news agnecy.
He said the people were killed by stray bullets in the shooting in the town of Bumba, 800 km from Kinshasa.
"The polling station was destroyed and a pro-Kabila radio station was attacked when the MLC supporters said there were already votes for Kabila in the ballot box before voting," he added. The MLC is Bemba's party.
The governor said the official election commission had denied there had been stuffing of ballot boxes.