European Union observers say Rwanda's presidential election was "not entirely" free and fair.
Ex-PM Twagiramungu does not accept the result
However, the head of the EU observers, Colette Flesch, said it was "an important step in the democratic process".
President Paul Kagame won 95% of the vote but opposition candidate Faustin Twagiramungu has rejected the results.
The vote was Rwanda's first democratic elections since the 1994 genocide in which 800,000 people were killed.
Earlier, Mr Kagame told the BBC there was no truth in Mr Twagiramungu's allegations, and the people of Rwanda were not complaining.
"People in Rwanda are very happy about the elections," he said.
Mr Kagame added that his victory would provide the country with a platform for stability.
Ms Flesch suggested that some ballot boxes may have been stuffed and some EU observers had not been welcomed as votes were counted.
"There was illegal manipulation of the list (of voters), as seen in the significant differences in numbers of people on voters lists and number of counted ballot papers in some polling stations," she said.
"There is still work to be done in terms of credibility, transparency and freedom of expression."
Earlier, the South African observer mission said the election had been free and fair.
Mr Kagame is an ethnic Tutsi who led the rebel movement which ended the slaughter of the Tutsi minority and moderate Hutus by Hutu extremists.
He has been credited by both the Tutsi and Hutu communities with promoting ethnic reconciliation after the genocide.
Critics say the opposition was virtually excluded from campaigning.
Mr Twagiramungu is a moderate Hutu former prime minister.
On the eve of the poll, 12 of his supporters were arrested for allegedly planning to "co-ordinate acts of violence" in the provinces.
"I do not accept this election... That's not democracy," he complained.
"They are trying to have a Stalinist style one-party system. Almost 100%? That's not possible. I will write a letter to the Supreme Court."
Other opposition members accused Mr Kagame's government of exploiting fears of a return to ethnic conflict to stifle dissenting voices.
On Sunday Alivera Mukabaramba withdrew from the race and advised her supporters to back Mr Kagame, her spokesman said.
Her withdrawal left only one other candidate in the race apart from Mr Twagiramungu - Jean Nepomuscene Nayinzira.
Correspondents say Mr Kagame is likely to face growing international pressure to use his new mandate to accelerate the process of democratisation in Rwanda.