President Yoweri Museveni has led the country since a rebel group he was aligned with seized power in 1986. A new term would give him five more years.
He had 71% with about a fifth of the votes counted, election officials said. Opposition front-runner Kizza Besigye had 22%.
Final results will be released in 24 hours, election officials said Saturday.
Museveni has vowed to quash any Egypt-like uprisings aimed at toppling regimes that have been in power for a long time.