According to the election commission, 76-year-old Yoweri Museveni has 58.9 percent of the people's support and Wine 34.6 when 91 percent of the votes are counted.
The final election result is expected during the day.
However, opposition leader Bobi Wine, whose real name is Robert Kyagulanyi, has dismissed the figures, saying widespread fraud had occurred.
Military presence
On Friday, the opposition candidate stated that his home was under siege and that his life was in danger.
- I have tried to leave my area and I am stopped by the military.
They say they have orders not to let me go, Bobi Wine told Reuters on Saturday.
But according to the police, it is only a matter of them stepping up their presence in Wine's residential area for his own safety.
However, according to witnesses, the security forces have also prevented international journalists from entering.
Internet closed
The government decided on Wednesday to shut down the internet and social media, which still does not work.
Bobi Wine and his followers have used Facebook for press conferences since he stated that many media companies did not want to receive him.
He has promised that video evidence of electoral fraud will be shared as soon as the internet connection works again.
"Inadequate"
The US and the EU have not had any observers at the election, but one of the people in charge of African affairs at the US Foreign Ministry, Tibor Nagy, writes on Twitter that the election process has been fundamentally flawed, and refers to reports of fraud, that observers have not been accredited as well as violence and harassment of members of the opposition.
The African Union (AU) and the East African Community have had observers on site, but no information on any irregularities has come from there.
The run-up to Thursday's presidential election has been one of the most violent in many years and many opposition supporters have been killed during the election campaign.