Police have named an Indonesian, Bahrun Naim, as the mastermind of Thursday's deadly attack in Jakarta's main business district after it arrested three men in a pre-dawn raid.

The arrests on Friday came less than 24 hours after the shooting and bombing rampage, the first such attack in the world's most populous Muslim nation since 2009, which killed seven people. Five of the dead were the attackers themselves.

Police said Naim, who spent one year in jail for illegal possession of weapons in 2011, funded the attack. He is now believed to be in Syria fighting for the Islamic State of Iraq and the Levant (ISIL).

"His vision is to unite all ISIS-supporting elements in Southeast Asia, including Indonesia, Malaysia and the Philippines," Jakarta police chief Tito Karnavian said.

The police chief of Depok, where the arrests were made, told Metro TV that the men - which he described as a bomb-maker, a firearms expert and a preacher - were not linked to the Jakarta attack.

Raids were also under way across other parts of the populous island of Java and on other islands to round up suspects behind the attack, Reuters reported.

"Now we are sweeping in and outside Java, because we have captured several members of their group, and have identified them," National Police spokesman Anton Charliyan told Reuters.

At least 20 people were wounded when at least five attackers opened fire near a Starbucks coffee house in the city. Those killed included an Indonesian and a Canadian.

Officials said the attackers were armed with light weapons and suicide belts. Six blasts occurred about 50 metres apart in the central business district, which also houses a United Nations office.

The attacks were claimed by the ISIL group in a statement on Thursday, in which the group claimed it had killed 15 people.

Al Jazeera's Sohail Rahman, reporting from Jakarta, said many circumstances surrounding the attacks on Thursday remained unclear.

"There's not a state of emergency but certainly a heightened level of alert ... three individuals are being questioned at the moment. Whether there were any that got away is one line of inquiry.

"Who are they, where did they come from, how did they get into Jakarta, who helped them get in, did anyone house them?

"The munitions that were used, the rifles and the explosives, where did all of that come from? That's what's being looked into by investigators."