By Agustinus Beo Da Costa and Eveline Danubrata

JAKARTA (Reuters) - Indonesian police on Monday urged Muslims to stay calm and not be "provoked" by the vandalism of a mosque in the capital, aiming to dispel fears of growing ethnic tension in the run-up to next year's election for the governor of Jakarta.

Over the weekend, white Christian crosses were found spray-painted at several locations, including on the green gates of the Al Falah Mosque in Jakarta, the largest city in the world's most populous Muslim-majority nation.

The incident risks fueling already simmering tension ahead of February's election, which pits the Christian and ethnic Chinese incumbent, Basuki Tjahaja Purnama, against Agus Harimurti Yudhoyono, a son of former president Susilo Bambang Yudhoyono, and the previous education minister, Anies Baswedan.

Yudhoyono and Baswedan are both Muslim in a nation where about 90 percent of the 250-million population follows Islam.

Indonesia also has a sizeable ethnic Chinese minority, many of whom are Buddhist. The country has a history of anti-Chinese violence, most sharply in the late 1990s amid the political and economic crisis that brought down authoritarian ruler Suharto.

Police were still looking for the vandal, Jakarta police spokesman Awi Setiyono said, adding that it was uncertain whether the act was linked to the election. "We urge the public not to be influenced and to control themselves."

Purnama, better known by his nickname "Ahok", became Jakarta's first ethnic Chinese governor in 2014, after then-governor Joko Widodo stepped down to successfully run for president.

Hardline Muslim groups had opposed his rise to power.

Purnama has a reputation as a tough reformer, but he has recently come under attack from several Muslim groups for allegedly insulting the religion's holy book, the Koran.

Muhammadiyah, one of the country's biggest Muslim organizations, had asked the police to investigate Purnama for alleged religious defamation.

During a visit to an Indonesian island last month, Purnama referred to a verse from the Koran that seemed to suggest it was unIslamic to vote for a leader of a different religion, according to a video circulated on social media.

"Insulting a religion and spreading hatred among Muslims is a criminal case," Pedri Kasman, an official at Muhammadiyah's youth wing, which filed the police report, told Reuters.

Purnama's words were taken out of context and incorrectly linked to religious defamation, said Mohamad Guntur Romli, an official of his election campaign. Political opponents had been fanning tension ahead of the election, he added.

Thousands of Muslims plan to stage a protest against the Jakarta governor on Friday, media have reported.

While most Indonesians are rational and will choose a leader based on merit, some camps would still vote along racial or religious lines, said Irine Gayatri, a political analyst at government body the Indonesian Institute of Sciences.

"Race and religion are a convenient tool that can easily be exploited by political opponents," she added.

(Reporting by Agustinus Beo Da Costa and Eveline Danubrata; Editing by Randy Fabi and Clarence Fernandez)