Zimbabwe's opposition leader has rejected the president's call for "national dialogue" after days of protests and a violent security crackdown, instead demanding an end to "terror" and the release of prisoners before any such talks.

"In order to dialogue, one’s tongue must be free to talk. The tongues of the nations are tied in jails and many others by fear. This must end," Nelson Chamisa, leader of the Movement for Democratic Change (MDC), said in a series of tweets.

The MDC accuses the authorities of a brutal crackdown against demonstrators fed up with high fuel prices and a failing economy.

But ministers say the MDC is using people's discontent as a pretext for violence.

President Emmerson Mnagagwa said earlier on Tuesday that a dialogue was necessary to "put the people first".