"Ebola spreads through contact. For the time being, people should resort to jambo (waving)," Museveni was quoted in the state-owned newspaper New Vision as saying. "If I don't shake your hand, it doesn't mean I don't like you."
On Friday, the government said suspected cases of Ebola -- most of them in western Bundibugyo district bordering Democratic Republic of the Congo -- had risen to 101. They included two in Kampala, one of them a doctor who died.
Another 338 people were being monitored because they came into contact with those infected by the virulent haemorrhagic fever.
Doctors say the virus can be passed through contact with an infected person.
The outbreak began in August and has spread panic since it was confirmed last week. Eleven health workers treating Ebola patients have contracted the disease. Four of them died.
Ebola is spread by contact with body fluids, including saliva. Kenya, Rwanda and Congo are screening travellers entering their borders with Uganda.
However, Ugandans remained free to move anywhere, raising fears that the disease could spread outside Bundibugyo, through the east African country's highly mobile population.
Uganda was last hit by an epidemic of Ebola in 2000, when 425 people were infected and just over half died.
This year, an outbreak in Congo -- where some of the first cases in 1976 gave the virus its name after the country's Ebola river -- infected up to 264 people, killing 187.