By Fransiska Nangoy and Nilufar Rizki

JAKARTA (Reuters) - An Indonesian suicide bomber believed to be a supporter of the Islamic State militant group attacked a police station in the city of Solo on Tuesday, killing himself and wounding a police officer, security officials said.

Indonesia has been on heightened alert since Islamic State claimed responsibility for its first attack in the Southeast Asian country last January in Jakarta, in which eight people were killed including the four attackers.

Shortly after Tuesday's attack, President Joko Widodo, who is from Solo and a former mayor of the city, urged calm and ordered police to arrest anyone who may have been connected to the bomber.

"I have asked the police chief to chase down the network and uncover who is the suicide bomber," the president told reporters.

"We hope people remain calm on this last fasting day. No need to be scared."

Police have stepped up security at churches, mosques, shopping malls and airports as Indonesia, home to the world's largest Muslim population, prepares to celebrate the end of the Islamic holy month of Ramadan.

Police said the attacker detonated the bomb he was wearing shortly after driving his motorcycle into the grounds of the police station in Solo, which is known as a hotbed of religious fundamentalism. A police officer who tried to stop him from entering sustained minor wounds.

Police said they believed the suicide bomber was Nur Rohman, a suspected follower of Bahrun Naim, an Indonesian fighting for Islamic State in Syria. Naim is believed to be one of the masterminds of the Jakarta attacks in January.

Security officials fear that Naim and other Islamic State leaders were now asking their supporters in Indonesia and in other countries to launch attacks at home, instead of being drawn to the fight in the Middle East.

"What is happening in Indonesia is a spillover of conflicts in the Middle East," Tito Karnavian, the of the National Counterterrorism Agency, told reporters in Solo.

Southeast Asian militants fighting for Islamic State in the Middle East have said they have chosen one of the most wanted men in the Philippines to head a regional faction of the radical group that includes Indonesians and Malaysians, security officials said last month.

(Additional reporting by the Jakarta bureau; Writing by Randy Fabi; Editing by Michael Perry, Robert Birsel)