* Mnangagwa cancels Davos trip after violent protests
* Says to punish any misconduct by security forces
* Rights commission says civilians tortured
* Hundreds detained, activists in hiding
* Fears Zimbabwe sliding back into authoritarian rule
* Fragile economy at heart of political turmoil (Adds detail, background)
By MacDonald Dzirutwe
HARARE, Jan 22 (Reuters) - Zimbabwe President Emmerson Mnangagwa promised on Tuesday to investigate violence against civilians who joined protests and punish any misconduct by security forces, as the country's rights commission said civilians were being systematically tortured.
Police say three people died during violent demonstrations last week, but human rights groups say evidence suggests at least a dozen were killed, giving rise to fears that - under Mnangagwa's leadership - Zimbabwe is sliding back into authoritarian rule.
The Zimbabwe Human Rights Commission (ZHRC) said on Tuesday security forces instigated systematic torture of residents following the violent unrest that erupted last week after a steep hike in the price of fuel. The level of force used on those who died or injured and supported by medical reports pointed to police brutality, a ZHRC commissioner told reporters.
In his first public comments since cutting short a foreign trip and returning to Harare late on Monday, the president said "violence or misconduct by our security forces is unacceptable and a betrayal of the new Zimbabwe."
"Misconduct will be investigated. If required, heads will roll," Mnangagwa wrote on Twitter on Tuesday, calling for a "national dialogue" involving churches, civil society and the opposition.
The unrest drove Mnangagwa to cancel an appearance at the World Economic Forum in Davos, where he had been expected to pitch for foreign investments, and fly home.
Hundreds of civilians, including activist pastor Evan Mawarire and opposition lawmakers, have been detained since demonstrations that were triggered nine days ago by 150 percent hikes in price of fuel decreed by Mnangagwa.
He said on Tuesday that that increase had been necessary.
'BEATINGS AT SAFE HOUSE'
Several opposition politicians and rights activists have gone into hiding as authorities try to track them down. Lawyers and ZHRC say security forces have raided homes of suspected protesters at night and beaten up occupants, charges denied by the police and army.
Zimbabwe Lawyers for Human Rights said police arrested 28 men late on Monday who were receiving treatment at a safe house after beatings by soldiers.
Police could not immediately comment on those arrests.
A spokesman for Mnangagwa, who became leader after long-time leader Robert Mugabe was forced out in November 2017, said on Sunday that the crackdown was a foretaste of how authorities would respond to future unrest.
That, along with an internet blackout, has fuelled fears that the country is sliding back into Mugabe-era authoritarianism. A judge on Monday ordered that communications shutdown to be rescinded.
Jacob Mafume, a spokesman for the opposition Movement for Democratic Change, said there was an urgent need for dialogue.
"The arrest of labour leaders and opposition members is a familiar script in Africa. We have called for dialogue until our voices have gone hoarse but have been ignored," Mafume said.
With high inflation and a shortage of cash in circulation eating into ordinary Zimbabweans' spending power, the fragile state of the economy is at the heart of the country's political problems.
A 14-day strike notice given by public sector unions expires on Tuesday. Apex Council, which represents all civil service unions, will meet on Tuesday or Wednesday to plan its next move, its deputy chairman Thomas Muzondo said. (Additional reporting by Alexander Winning in Johannesburg Editing by James Macharia and John Stonestreet)
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