Fourteen people have died, including one in Kampala, since the outbreak began in western Uganda three weeks ago.Ebola is one of the most virulent diseases in the world.
It is spread by close personal contact and kills up to 90% of those who become infected.
Seven doctors and 13 health workers at Mulago hospital - the main referral hospital in Kampala - are in quarantine after "at least one or two cases" were taken there.
"I wish you good luck, and may God rest the souls of those who died in eternal peace," Prez Museveni said as he ended his address to the nation.
The first victim of the latest outbreak was a pregnant woman in Kibaale district, about 170km (100 miles) west of Kampala.
It then spread at a funeral, Mr Museveni said.