Early indications on Wednesday showed former Education Minister Anies Baswedan as winning the Jakarta gubernatorial election.
According to the polling company Indikator Politik, Baswedan led incumbent Basuki Tjahaja Purnama by 58 percent to 42 percent.
The official results in the contest, which has been riven by sectarian tensions, are due next week.
Purnama, an ethnic Chinese Christian backed by the ruling Indonesian Democratic Party of Struggle, conceded defeat and called for unity at a news conference in Jakarta.
"To my supporters -- believe that God gives and takes power," he said in comments broadcast by Metro TV.
Baswedan, who is supported by the opposition Gerindra Party and Prosperous Justice Party, called on voters to forget the differences of the campaign, which has seen Purnama put on trial over blasphemy allegations. He denies intending to insult Islam.
"This is a new chapter," Baswedan said, according to the kompas.com news website. "After there is competition, it continues with cooperation. We are ready to continue."
Purnama stressed that he still has six months in office and promised to help Baswedan's transition.
His trial, in which he faces a five-year jail term, is due to resume on Thursday. His alleged blasphemy led to thousands of people protesting against his candidacy during the campaign. -