HARARE (Reuters) - Zimbabwe has charged 68 people with public violence following violent clashes between protesters and the police last week and a magistrate court will on Tuesday rule whether they should be released from custody while they await trial.

Police fired tear gas and water cannon at opposition leaders and hundreds of demonstrators at Friday's protest before unrest swept across large parts of the capital, Harare.

The 68, who include a freelance photographer, first appeared in court on Saturday. Accused of burning property, attacking police officers and looting shops, they were not asked to plead.

They face a fine and up to 10 years in jail if convicted.

Around 100 riot police stood outside the court house in downtown Harare, accompanied by water cannon and armored cars. Officers blocked relatives of the accused and members of the public from getting in.

Police arrested three people waving banners criticizing 92-year-old President Robert Mugabe, who is facing rising public anger at the dire state of the economy, in particular shortages of cash and unemployment estimated at over 80 percent.

Defense lawyers will argue that those arrested last week were innocent people caught up in the violence.

Magistrate Tendai Mahwe earlier refused bail for political activist Promise Mkwananzi and another man charged with public violence following a protest by opposition youths on Aug. 24.

Mkwananzi is linked to the social media movement #Tajamuka, which joined forces last month with the #ThisFlag campaign of pastor Evan Mawarire to organize a 'stay-at-home' protest billed as the biggest strike in Zimbabwe since 2007.

Mahwe ruled that Mkwananzi faced serious charges and should not be freed on bail. His lawyer, Tonderai Bhatasara, said he would appeal the ruling at the High Court.

(Reporting by MacDonald Dzirutwe; Editing by Ed Cropley)