Museveni blamed drought in the east African country for the rising food prices and said international events had pushed up the price of oil.
“There will be no demonstrations in Kampala … if Besigye wants to walk for exercise let him do it somewhere else,” Museveni told a media conference at his rural home southwest of the capital.
“If Besigye demonstrates, will it bring international oil prices down because he has demonstrated? Will it rain because Besigye has demonstrated?” said Museveni in his first public reaction to the protests.
Prices have been rising after drought cut food output across Uganda, while higher global oil prices have increased transport costs, pushing up food prices further in urban areas.
The consumer price index jumped 4.1 percent in March from February, pushing the year-on-year inflation rate to 11.1 percent, the fifth straight rise.
Security forces on Thursday fired rubber bullets and teargas to disperse a crowd of more than 1,000 led by Besigye, Museveni’s closest rival in February elections.
Besigye said he was injured in the march to the centre of Kampala after a rubber bullet struck his finger.
Protests were also reported in the second busiest commercial town of Jinja in eastern Uganda, Masaka in south western Uganda, and Gulu to the north, epicentre of a now fizzled-out two-decade rebellion.
“SAVE FUEL, DON’T DRIVE TO BARS”
“Demonstrations will worsen the situation because business people will be scared to transport food and fuel to the city because their vehicles will be burnt,” said Museveni.
“Some people have been saying we should remove the tax on fuel, but the tax is small and we need this money to build roads and if we removed this tax we would be subsidising consumption.”
Museveni urged Ugandans to be frugal with oil consumption.
“What I call on the public to do is to use fuel sparingly, don’t drive to bars,” said Museveni.
After losing in February elections, Besigye called for peaceful protests against Museveni’s 25-year-old rule, saying the poll had been rigged, but they failed to get off the ground.
While campaigning, he said east Africa’s third largest economy that has struck oil was ripe for an Egypt-style revolt.
Besigye said he was not calling for processions, but simply asking people to walk to work two times a week to show solidarity with the poor.
Opposition and civil society groups launched their first “walk to work” protest against steep rises in the cost of living on Monday but it was swiftly stifled by police, and opposition leaders were detained. Besigye was charged with inciting unrest.
Many Ugandans complain of worsening poverty, but others respect Museveni for bringing stability to a country once plagued by brutal despots such as Idi Amin.