Jakarta's incumbent Christian governor Basuki Tjahaja Purnama has conceded defeat in the race to become the city's new governor after unofficial results showed former Indonesian education minister taking the polls.

So-called quick counts by 10 research companies on Wednesday showed Anies Baswedan, a former cabinet minister, winning 58 percent of votes in the head-to-head vote, with 100 percent of ballots counted.

The official results will be announced by the national elections commission early May.

In his concession speech, Purnama, also known as Ahok, urged his supporters to stay calm.

"To our supporters, I know you are sad, but this is the will of God," Purnama said.

"We still have six months to finish our homework and we will do our best," he said, referring to his time left in office.

The vote followed a campaign that opened religious and racial divides in the world's most populous Muslim nation.

Purnama was Jakarta's first Christian governor in half a century and the first ethnically Chinese governor.

He had been popular with middle-class Jakartans for his efforts to stamp out corruption and make the overflowing polluted city more livable. But his brash manner and evictions of slum communities alienated many in the city of 10 million.

He is on trial for blasphemy. In recent months, hundreds of thousands of Indonesians have protested against him in the capital, deriding his Chinese ancestry and calling for him to be imprisoned or killed.

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On Thursday, prosecutors will make their sentencing demand in Purnama's trial.

Blasphemy is a criminal offence in Indonesia and punishable by up to five years in prison.

Baswedan, a highly educated Muslim politician, capitalised on the backlash against Purnama by courting the support of conservative religious leaders and figures on the radical fringe who opposed electing a non-Muslim.

The polarising campaign has given Indonesia's conservative Muslim groups a national stage.

Purnama won the first round in February but not by a big enough margin to avoid a runoff.