Dr Besigye earlier threatened to call street protests if he felt the process was not free and fair.
The governing party has been accused of using state resources to bribe voters.
Although the presidential race was largely peaceful, there were several clashes between supporters of rival candidates in the parliamentary elections.
Mr Museveni has vowed to stop any Egyptian-style street protests and lock up any demonstrators.
'Corrupt and repressive'
Dr Besigye told reporters that he would consult with his allies on Sunday to discuss the next move.
Dr Besigye has attracted significant support from Ugandans who are disgruntled with the current leadership but a divided opposition has helped Mr Museveni.
The advantage of incumbency was also great. The governing party, which spent a huge amount of money on the campaign trail, is accused of using state resources to bribe voters.
Some analysts warn that the economy is bound to take a significant hit because of the money pumped into the president's campaign.
He added that his coalition's own poll tally had been disrupted by the government blocking its text message system for collecting results.
The opposition candidate was standing against Mr Museveni for the third time.
Dr Besigye and Mr Museveni were allies in the guerrilla war which brought the latter to power in 1986, but they later fell out.
Mr Museveni has defeated his challengers every five years since 1996, though his support was steadily declining before this election.
In 1996, he received about 75% of the vote, but this fell to 59% in 2006.
The European Union's chief election observer said he was generally happy with what he had witnessed.
"We are glad to observe that no significant violence has taken place and the process is done in a peaceful manner," Edward Scicluna
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