The UN and former Colonial Power the UK both expressed concern about the violence, in which three people were killed after troops opened fire.
Parliamentary results gave victory to the ruling Zanu-PF Party in the first vote since the removal in November of long-time leader Robert Mugabe.
But the Opposition says Zanu-PF has rigged the election.
The result of the presidential vote is not yet known.
The Opposition MDC Alliance insists its candidate, Nelson Chamisa, beat the incumbent President Emmerson Mnangagwa.
Zanu-PF, which has been in power for 38 years since the country gained its Independence, denies there has been any rigging and has called for calm.