Eleven candidates, including the incumbent President Joseph Kabila, are contestants in the election.
About 32 million voters are eligible to vote in the second presidential election in the central African country since the end of civil wars.
There had been fears that the elections would be delayed because of the weekend's violence among supporters of rival contestants. According to local reports, at least four people died in clashes on Saturday.
However, main opposition leader Etienne Tshisekedi said that more than ten people were killed and 68 others were injured.
The violence compelled the police to ban final campaign rallies.
The United Nations, the African Union and the European Union called for restraint in the African country after the deaths.
President Joseph Kabila, who won the first post-war election in 2006, is tipped to win the elections.
Former Prime Minister Tshisekedi boycotted the 2006 elections, which were marred by violence.
He also accused international players of being against him.
"The international community has supported Africa's worst dictatorships for 51 years," he said.
Meanwhile, UN Secretary General Ban Ki-moon called on all political leaders and the people to show restraint throughout the election process.
Over 70 percent of Congo's 71 million people live in poverty despite the fact that the country has extensive and diverse mineral reserves.