Indonesian police said on Wednesday they will investigate a blasphemy complaint by Muslim groups against the Christian governor of Jakarta, amid simmering religious and ethnic tension in the world's largest Muslim-majority country.

The decision to officially name Basuki Tjahaja Purnama a suspect means the case will definitely go to court and is likely to stoke concerns over rising hardline Islamic sentiment.

But dropping the case could have sparked further protests by some Muslims against Purnama and also against President Joko Widodo, who is seen as a key backer of the ethnic Chinese governor.

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

Hardliners had also demanded Purnama's arrest, but police decided against detention because investigators' opinion on the case was divided. He was barred from leaving the country.

Ari Dono Sukmanto, chief of the police criminal investigation department, told reporters that "the dominant opinion is that this case should be settled in court".

Police said investigators would further question Purnama and compile a dossier to hand over to prosecutors who will then take the case to court.

"The process usually takes two months. The police chief has instructed the process be sped up," national police spokesman Boy Rafli Amar told Reuters.

Purnama faces up to five years in prison if found guilty.

Some analysts said the decision to pursue the case was a blow to democracy.

"It sets a bad precedent for minorities as the legal process can be dictated by public pressure," said Irine Gayatri, political analyst at the Indonesian Institute of Sciences.

Indonesia recognizes six religions and is home to several minority groups that adhere to traditional beliefs.

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

A social media user edited and subtitled a video of the speech but omitted a key word in the subtitles so it appeared the governor was criticizing the Koran rather than his rivals, police say.

The video went viral and incensed moderate and hardline Muslim groups alike.

The governor has denied blasphemy but apologized for the comments.

"I accept the status of suspect and believe in the professionalism of the police," Purnama told reporters.

"This is not just a case about me but about determining the direction this country is going in," he said, adding that he would continue to contest the Jakarta election.

Hardline Muslim groups have demanded that he resign.

"Muslim groups and people will continue to safeguard this legal process... Blasphemy by anyone against any religion amounts to intolerance and anti-pluralism," said Din Syamsuddin, a member of the moderate Muslim group Muhammadiyah and Indonesia's top clerical council.

In a joint statement with other Islamic groups, he called on Muslims to restrain themselves during the process.

Presidential spokesman Johan Budi urged all sides to respect the police decision.

"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, has plummeted during the controversy, according to an opinion poll published last week.