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Indonesia's President Joko Widodo has called off his visit to Australia after violent clashes at a Jakarta rally by thousands of hard-line Muslims.

Mr Widodo, also known as Jokowi, blamed "political actors" for exploiting the situation as protesters marched against Jakarta's governor.

The demonstrators accuse Basuki Tjahaja Purnama, a Christian, of having insulted Islam's holy book, the Koran.

The clashes left one person dead and 12 wounded.

"We deplore the incident," Jokowi said as he called for calm on the streets of the country's capital.

, Australian Prime Minister Malcolm Turnbull confirmed that the Indonesian president had postponed his visit.

It comes after Indonesian police used tear gas and water cannon to subdue protesters who refused to disperse after Friday prayers as they congregated around the presidential palace.

Police had been braced for the possibility of religious and racial tensions erupting at the rally, attended by an estimated 50,000 people.

It had mostly been peaceful but groups of angry demonstrators clashed with police after nightfall and set vehicles alight.

A Muslim group, the Islamic Defenders' Front, has accused Mr Purnama of insulting Islam after he said his opponents had used a verse from the Koran to deceive voters.

The verse can be interpreted as meaning that Muslims should not choose non-Muslims as leaders.

The protest was held to demand that Mr Purnama be prosecuted for blasphemy over the comments.

Mr Purnama has apologised but formal complaints have led to an investigation by police.

Muslims are the majority in Indonesia which has a population of 250 million.