 Police fired live rounds during the disturbance |
A suspected looter was shot by guards, a passer-by was hit by a stray bullet and an Asian man was stoned to death, while police have fired live bullets.
There have been several attacks on Asians in Kampala, and a Hindu temple has been damaged.
The sugar firm which wants to use part of the Mabira forest is Asian-owned.
Environmentalists say the move threatens the existence of rare species of trees and birds in the 30,000 hectare forest.
'Frightening'
The march began quietly, with some 1,000 people marching through central Kampala, carrying placards and tree branches.
"People were demonstrating peacefully when there was a misunderstanding with the police. All of a sudden they opened fire," environmental activist Frank Muramuzi told Reuters news agency.
The BBC's Sarah Grainger in Kampala says protesters threw stones at the police and set fire to vehicles.
An Asian motorcyclist was attacked and later beaten to death, witnesses say.
Our correspondent says the demonstration took on a racial dimension with some protestors blaming the country's Asian-Ugandan population for the situation because the parent company of the sugar firm, Mehta Grou, is owned by an Asian Ugandan.
Reuters also reports that police had to rescue about 40 men from a Hindu temple after it was attacked by a mob.
 Some Asian residents were targeted by the protesters |
"We were inside the temple and the protesters started attacking us from outside," 50-year-old Dipaul Patel told Reuters. "It was very frightening."
A police source says about 20 people have been arrested.
The Sugar Corporation of Uganda (Scoul), part of the Mehta group, wants to expand its plantations in central Uganda, taking over one-third of the Mabira forest.
Campaigners are now calling on Ugandans to boycott its sugar products.
In recent years, Ugandan Asians, including the owners of Mehta, have started to return to the country, after being expelled by Idi Amin in the 1970s.
They used to control much of the economy, sparking resentment among some Ugandans.
Text campaign
Parliament is yet to change the status of the forests and campaigners have threatened legal action if the forest is given away.
 The police blocked the protesters |
Public protests over the government plans have heightened in the capital and car bumper stickers urging people to save Mabira forest have become very popular, our correspondent says.
There has also been a text message campaign, urging people to take part in the protests.
Supporters of Scoul's bid for more land say the expansion of would create more jobs and income for the country.
They dismiss those opposing the move saying subsistence farmers have already encroached on much of the forest land.
The kabaka, or king, of the local Buganda community has offered to give alternative land for the sugar company in a bid to save the hardwood forest.
