"Uganda Decides," the New Vision newspaper headline read. "Your vote counts," the Daily Monitor front-page said.
Voting was due to begin at 07:00 am (0400 GMT), but despite queues forming outside polling booths, many were delayed opening for over an hour waiting for ballot papers.
Social media, including Facebook and Twitter, were inaccessible on voting day although Internet-savvy Ugandans dodged the apparent shutdown using virtual private networks (VPNs).
Museveni faces a challenge from seven candidates, but is widely predicted to win a fifth term, with the 71-year-old former rebel fighter who seized power in 1986 entering his fourth decade in power.
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"You have to be here on time because many people will be coming when the polling centre opens that means you will wait longer than one who came early like me," Musoke said.
"I came ready -- I packed tea and pancakes to wait until I vote."
In the Kololo district of the capital Kampala, around 50 people waited to vote, but election officials had not turned up, an hour after polling was meant to have begun.
"He has to change things like health, hospitals and roads," Karim said, as he waited for the polling station to open, criticising the delay in starting to vote.
Over 15 million Ugandans are registered to vote, casting ballots in over 28,000 polling stations for both a president and members of parliament, with 290 seats being contested by candidates from 29 political parties.
Over 150,000 police, soldiers and other security forces have been deployed to ensure tight security, election officials have said.
Polls are due to close at 04:00 pm (1300 GMT).