However, in the capital Kinshasa, the two main contenders and international observers remained satisfied with the way the election has been handled.
Azaria Ruberwa, who is also one of four vice presidents, alleged "massive fraud" in the presidential election, mostly in favour of incumbent Joseph Kabila. He demanded a new vote be held "in all polling stations where serious irregularities were noted".
Mr Ruberwa, head of the Congolese Rally for Democracy (RCD), a former Rwandan-backed rebel group, accused "representatives of the CEI (Independent Electoral Commission) of acting like political militants".
He claimed there were irregularities in the capital Kinshasa, as well as in the east of the country, the centre, the northeast and the southeast.
On Monday several minor candidates, including the son of former dictator Mobutu Sese Seko, also alleged serious irregularities in Sunday's presidential and parliamentary elections.
They are the first multi-party elections since the eve of independence from Belgium 46 years ago.
But the two leading candidates, Mr Kabila and rebel-turned-politician
Jean-Pierre Bemba, still appeared to be happy with the polls.
International observers also continued to urge candidates to respect the outcome and lodge any complaints via official channels.
A spokesman for Mr Kabila said that it was up to the DRC's Supreme Court to rule on complaints.
The United Nations mission in DR Congo said on Tuesday that the election had been "satisfactory".
"Some difficulties of a logistical nature, as well as some isolated incidents were certainly deplored, in particular in the two provinces of Kasai and Kinshasa. But overall the results are satisfactory and sometimes went beyond all expectations," it said.
The Carter Center, the human rights group founded by former US president Jimmy Carter which sent a 58-member team to observe the elections, said that the irregularities "appear to be minor".
However, some deficiencies in procedures had weakened important safeguards designed to verify voters' identities, it said.
A foreign diplomat in Kinshasa said that the fraud allegations were from candidates on the losing side frightened of losing power.
"They are realising that they are going to disappear from the political landscape," he said on condition of anonymity.
By early Tuesday ballots in 90 percent of districts had been processed and results posted on the doors of polling stations, CEI vice president Norbert Basengezi said.
The final nationwide count is not expected for three weeks though, because voting was still underway in some districts and because the DRC's vast size and weak infrastructure are slowing down the nationwide count.