Indonesian police said on Wednesday they will proceed with an investigation into a blasphemy complaint brought by Muslim groups against the Christian and ethnic Chinese governor of Jakarta and banned him from leaving the country.

The complaint against Basuki Tjahaja Purnama, nicknamed "Ahok" and the first ethnic Chinese and Christian governor of the sprawling Indonesian capital, comes as President Joko Widodo tries to keep a lid on security and simmering religious tensions in the world's biggest Muslim-majority nation.

Ari Dono Sukmanto, chief of the National Police criminal investigation department, told reporters that, although there had not been consensus after an initial investigation, "the dominant opinion is that this case should be settled in court".

Purnama would not be allowed to leave Indonesia during the investigation, police said.

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A decision to drop the case could have sparked mass protests led by hardline Muslims against not just Purnama but also Widodo, who is seen as a key backer of the governor.

The blasphemy allegations centre on a speech Purnama made in September in which he said his opponents had deceived voters by attacking him using a verse from the Qur'an.

Purnama has apologised for the comments but hardline Muslim groups have demanded that he resign, claiming that he insulted the Koran.

More than 100,000 Muslims marched against him this month, urging voters not to re-elect him in February.

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Presidential spokesman Johan Budi called for all sides to respect the decision by police to proceed with the case.

"From the beginning, the president has said he would not intervene," Budi said.

Support for Purnama, a Protestant once hugely popular for his tough, reformist approach to running the city of 10 million people, has plummeted during the controversy.