On Friday, police also named one of the five attackers who died in the assault that killed two people and wounded 24 more.
Convicted militant Afif, who also went by the name Sunakim, had been seen in photos that circulated in the news media. He was armed with a gun and was wearing jeans and a black shirt. He was carrying a rucksack with a bomb inside, police said.
Police were looking for further suspects. "We think there were five (attackers), but they must have had some support," said Police Chief Badrodin Haiti. CNN Indonesia showed video of police stopping cars at multiple checkpoints, checking them and questioning occupants.
The alleged mastermind, Bahrun Naim, is no stranger to Indonesian authorities, the police chief said. He was apprehended in 2010 for illegal possession of ammunition and was brought to justice. Naim was sentenced to at least 2½ years in prison.
The militant then left Indonesia, and is in Raqqa, "as part of the high ranks of ISIS," Karnavian said. ISIS claimed responsibility for the Jakarta attack in an official statement posted online.
Naim has formed a Southeast Asian branch of ISIS named Katibah al Nusantara, Indonesia authorities said. His vision is to join, to unite all ISIS supporting elements in Southeast Asia, including Indonesia, Malaysia and the Philippines.
Blast, murders, gunfight
The attack began Thursday morning with a suicide explosion near a Starbucks cafe on Thamrin Street, an entertainment and shopping district with various Western chain restaurants and stores.
"There were five small bombs and one big one," Haiti said. "The type is still being determined in the forensic laboratory."
Then two militants outside the coffee shop seized two people -- one of them a foreigner -- dragged them into a parking lot and shot them, said Charliyan, the Jakarta police spokesman.
They also opened fire at people on the street. One of the injured was also a foreigner.
Angele Samura, the security adviser for the Netherlands Embassy in Jakarta, said a Dutch national underwent surgery after being "severely injured." It's not known if this is the same Dutch citizen and U.N. Environment Programme worker who that agency reported was hurt.
Five attackers die
Heavily armed police soon swarmed the scene, firing on the militants and looking for other attackers.
The attackers responded by firing back and tossing two grenades at the officers, according to Charliyan. Minutes later, two more rode a motorcycle toward a nearby police post and blew themselves up.
Five attackers died in the firefight.
Police discovered several unexploded munitions, some of them high-grade explosives, at the scene.
A day after the attack, wreaths and tributes, expressing condolences to the victims and defiance against those who attacked, were stacked against the nearby police outpost.
Many bear the slogan #KamiTidakTakut
, which translates to "We are not afraid." Indonesians took to social media under the hashtag to show defiance in the face of terrorism.
The small number of people laying tributes outside the coffee shop and police outpost told CNN they had rarely seen the bustling, 24-hour street so quiet.
Boni Marlen, a 22-year-old studying law, rode up to the scene on a mountain bike late Thursday and shook his head.
"I want to be near the people who died to pray for them," he said, repeating the slogan, "We're not afraid." He said the extremists counted as only a small group. "We must fight them."
Last major attack 2009
The capital of Indonesia, a country which is home to the world's largest Muslim population
, hasn't seen an a major militant attack in six years.
Since then, the secular government has made major inroads beating back terror groups in an Asian nation.
Returning ISIS fighters?
In recent weeks, Indonesian police have been on high alert, while military operations focus on hitting the East Indonesian Mujahadeen, helmed by Indonesia's most-wanted terrorist, Santoso, who has pledged support for ISIS.
One major worry is that Indonesians fighting in Syria and Iraq will return home, having gained training and combat experience.