On Wednesday afternoon, Baswedan stated that he was open to an arrangement with Agus Yudhoyono to secure his votes for the second round in April.
Political analysts had anticipated that the election would go into the second round due to the three-cornered contest - among incumbent Basuki Thahaja Purnama, Anies Baswedan and Agus Harimurti Yudhoyono, and their running mates for vice-governor.
Wednesday's election - one of hundreds of regional ballots taking place across the country - exposed sharp religious and social divisions, overshadowing the many pressing social issues facing the capital.
However, preliminary results show that the current Chinese Christian of Jakarta, Basuki Tjahaja Purnama might have a narrow lead over his opponent.
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The blasphemy trial and the ease with which hard-liners attracted several hundred thousand to protest against Mr Purnama in Jakarta in November and December a year ago have undermined Indonesia's reputation for practising a moderate form of Islam and shaken the centrist government of President Joko Widodo (also known as "Jokowi"). Popular with middle-class residents for his efforts against corruption and to improve the quality of life, accusations against him of blasphemy - a criminal offense - surfaced in September and he is now on trial.
Opponents seized their moment previous year when a video surfaced of Mr Purnama - also known as "Ahok" - telling voters they were being deceived if they believed a specific verse in the Quran prohibited Muslims from electing a non-Muslim as leader.
Basuki has been involved in an ongoing criminal trial on the charge of blasphemy against Islam over allegedly insulting a verse in the Quran referred to as "Surah al-Maidah: 51" that implies Muslims should not be governed by non-Muslims. If convicted, he faces a maximum five-year jail sentence, though could still govern while appeals are heard.
Baswedan often wears a white shirt and a black Muslim cap while campaigning, while Yudhoyono tends to be more casual in a black polo shirt.
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Roughly 190 million Muslims live among Indonesia's 250 million citizens that also include minority Christian, Hindu and Buddhist populations.
Most observers are warning that any run-off between Governor Purnama and Anis Baswedan could inflame religious tensions further.
The official result will not be known until early March but according to quick count results, which have proven accurate in the past, Ahok was narrowly leading Anies with 43 per cent of the vote after a peaceful polling day.
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"In an election campaign you need to bring everyone together and reach out to all groups". We wanted to secure one round victory.