About 100 supporters of Hakainde Hichilema's party outside vote-counting centre driven off with batons and tear-gas.
A number of Hakainde Hichilema's United Party for National Development supporters waiting for results of the closely fought race were arrested and forced into a police van on Wednesday, an AFP news agency reporter said.
The group had kept a vigil outside a conference centre in Lusaka where the first batch of official results from Tuesday's vote were expected to be released.
Al Jazeera's Haru Mutasa, reporting the scene of the confrontation
