At least eight people were killed in a stampede on Monday as thousands of desperate Zambians scrambled for food handouts, police said.

The incident occurred in the capital Lusaka at a public sports centre where a church was handing out food to about 35,000 people, mostly from the city's impoverished slums.

"Eight people died while 28 others were injured in a stampede which happened at the Olympic Youth Development Centre around 6:00 am (0400 GMT) today as a crowd jostled to enter the premises," police said in a statement.

"The victims are among the 35,000 which the group had invited for prayers."

Police ordered the church that had been distributing the corn meal, cooking oil and salt, to halt the handouts.

Hundreds of people, however, stayed there hoping the organisers would resume distribution, with some saying that the country's president should ask millers to cut meal prices.

"We cannot afford to buy it, so we come here," Memory Chisanga, a 64-year-old woman, told AFP.

A member of the church declined to comment.

Southern Africa has been hit by a severe drought since 2015, and food prices in Zambia have risen steeply.