Islamic Defenders' Front which led the demonstration says Basuki Purnama misrepresented a Quranic verse. Nahdlatul Ulama, a powerful Islamic body, has asked Muslims to forgive the governor's "slip of tongue".
Thousands of Indonesian Muslims on Friday protested against Jakarta's governor for allegedly insulting their religion. The demonstration fuelled tensions ahead of the governor's re-election bid in February.
Governor Basuki Tjahaja Purnama, better known by his nickname "Ahok," became Jakarta's first ethnic Chinese governor in 2014. Some Muslim groups opposed his rise to power. He came under fire recently for allegedly making inaccurate representations about the Holy Quran.
"I hope all law enforcement will punish Ahok for what he had done as he has insulted our Prophet, and he also insulted the Quranic verses," one protester, Hiday At, said.
Surrounded by military and police forces, thousands of protestors dressed in white chanted anti-Ahok slogans and held banners demanding his execution. The demonstration was initiated by Islamic Defenders' Front (FPI). The FPI was one of the groups that protested against Purnama's elevation to governor in 2014. The group is known for reacting with violence to views which offend their vision of Islam.
Purnama, during his visit to an Indonesian island last month, referred to a verse from the Quran that seemed to imply it was unIslamic to vote for a leader of a different religion, according to a video circulated on social media.
Purnama has since apologised but denied any wrongdoing, saying the video was edited.
"It is clear, and you can see from the original video, I had no intention to insult Islam," Purnama told reporters at his office ahead of the protest.
Indonesia's biggest Islamic group with 40 million members, the Nahdlatul Ulama, did not support Friday's demonstration.
A senior official at Nahdlatul Ulama, Ahmad Ishomuddin, said his organisation did not support the protest and that the violence went against Islamic teachings.
"This could be dangerous," Ishomuddin said, urging Muslims to remain calm and to forgive Purnama over the recent comments. "Ahok, whose tongue slipped, has apologised."
Indonesia is the world's largest Muslim-majority nation, priding itself as a peacemaker, and the vast majority of its population practice some form of the religion.