So far, the death toll across the country from the Ebola epidemic declared in late September has climbed to 44, according to World Health Organisation figures issued last week.
Uganda's health ministry meanwhile says there have been 90 confirmed cases overall, and 28 deaths.
Health Minister Jane Ruth Aceng said in a tweet "Fellow Ugandans, let's be vigilant. Report yourself if you have had contact or know of a person who has had contact."
President Yoweri Museveni earlier this month ordered Kassanda and Mubende, the epicentre of the outbreak, to be put under lockdown, imposing a travel ban, a curfew and the closure of public places.
But Aceng told AFP Monday: "The situation in Kampala is still under control and (there is) no need to restrict people's movements."
Residents of the capital, a city of about 1.5 million people bordering Lake Victoria, said they were anxious.
"It is getting scarier now that Kampala is recording Ebola cases," said Rebecca Nanyonga, a 27-year-old mother of two.
"The government has not done much to sensitize Kampala residents on Ebola," she said. "Parties and music concerts are still held yet the disease is in our midst."
The virus that is circulating in Uganda is the Sudan strain of Ebola, for which there is no proven vaccine, unlike the more common Zaire strain that spread during recent outbreaks in neighboring Democratic Republic of Congo.
The outbreak began in September in a rural part of central Uganda. It spread earlier this month to Kampala, a city of more than 1.6 million people, by a man who had come from the Kassanda district to seek medical treatment and later died.
Health ministry spokesperson Emmanuel Ainebyoona said all of the patients in Kampala were in isolation when they became symptomatic, reducing any chance of them passing on the virus.
There have been more than 90 confirmed and probable cases in Uganda since the start of the outbreak, including at least 44 deaths, according to statements by the health ministry and the World Health Organization.
Ebola generally kills about half of the people it infects. Its symptoms include intense weakness, muscle pain, headaches and a sore throat, vomiting and diarrhoea.
