But his main challenger, pop star-turned-politician Bobi Wine, said that tally was the result of the worst rigging in Ugandan electoral history.
Election monitors say confidence in the count has been damaged by an internet shutdown, now in its third day.
Dozens of people were killed in the run-up to the election.
President Museveni, who has been in power for 35 years, is hoping for a sixth term.
The 76-year-old says he is standing for stability, while Bobi Wine, the stage name for 38-year-old Robert Kyagulanyi, says he represents the younger generation in one of the world’s youngest countries.
What are the latest results?
With 29.4% of ballots counted, Mr Museveni has won 63.9% of the vote compared to Bobi Wine with 28.4%, Reuters news agency quotes the electoral commission as saying.
Earlier, election commission chief Simon Byabakama said the vote had been peaceful, hailing it as a success.
The results were being transmitted to a tallying centre despite the internet not working, he said.
“We’re not using local internet to transmit results. We are using our own system. Don’t worry, the results will come in spite of the fact that internet has been shut down,” he told journalists.
But Bobi Wine, who said some of his polling agents were arrested on Thursday, believes the shutdown is being used to block communication and as a way of compromising the vote.
As well as being unable to get online, people have been having trouble sending text messages.
“I will be happy to share the videos of all the fraud and irregularities as soon as the internet is restored,” Reuters quoted him as saying.
The electoral commission says only two polling stations in the country reported major irregularities and voting was cancelled there.
BBC correspondents say there is tight security in the capital, Kampala, with soldiers and police patrolling the streets.
It has been quiet in the city on Friday morning and some businesses remain closed, the AFP news agency reports.