During Thursday’s vote, voting was delayed by up to four hours in many polling stations as ballot boxes were slow to arrive and biometric machines, used to verify voters’ identity, did not work properly.
Some have linked the problems to the internet blackout.
Election chief Simon Byabakama said on Friday that the vote counting had not been affected and final results would be out before 17:00 local time (14:00 GMT) on Saturday.
President Museveni, 81, is seeking a seventh term in office. He first took power as a rebel leader in 1986.
Wine, a 43-year-old pop star-turned-politician, says he represents the youth in a country where most of the population is aged under 30.
He has promised to tackle corruption and impose sweeping reforms, while Museveni argues he is the sole guarantor of stability in Uganda, a country with a history of conflict.
Although there are six other candidates, the presidential poll is a two-horse race between Museveni and Wine.
The campaign period was marred by the disruption of opposition activities – security forces have been accused of assaulting and detaining Wine’s supporters.
Rusoke, the police spokesperson, dismissed these complaints, accusing opposition supporters of being disruptive.
Internet access was suspended on Tuesday, with Uganda’s Communications Commission saying the blackout was necessary to prevent misinformation, fraud and the incitement of violence – a move condemned by the UN human rights office as “deeply worrying”.