Karnavian spoke to CNN one day after the violence erupted midday, killing at least two, wounding 24 and raising alarm about terrorism in the world's most populous Muslim country.
"We have been informed by our intelligence that an individual named Bahrun Naim, based on the communications ... instructed his cells in Indonesia to mount an attack in Indonesia," Karnavian said.
Naim, who police believe is living in Syria, was apprehended by Indonesian authorities in 2010 for illegal possession of ammunition and was brought to justice, the police chief said. 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.
"He created cells or a branch of ISIS named Katibah al Nusantara. His vision is to join, to unite all ISIS supporting elements in Southeast Asia, including Indonesia, Malaysia and the Philippines," the chief said.
Police spokesman Anton Charliyan had said earlier that Naim is in Syria but sent money back home to Indonesia to finance the attack.
A blog containing ISIS teachings likely belongs to Naim, according to an Indonesian anti-terror source.
The blog contains posts written in the Bahasa Indonesia language on how to conduct terror attacks, lessons learned from the Paris attacks, how to avoid intelligence surveillance, how to make homemade pistols and how to conduct guerrilla warfare in cities, among others.
Authorities in Indonesia have been monitoring the blog for two years, the anti-terror source said. He added it's "highly possible" the blog is run by Naim himself or by people posting on his behalf.
Karnavian said the difference between ISIS and terror groups formerly active in Indonesia, such as Jemaah Islamiyah and al Qaeda, is that the former is more dangerous because its ideology allows it to kill Muslims in a way that previous groups did not.
As the sun broke the day after the attack, corrugated iron covered the shattered windows of the Starbucks that had been the scene of so much destruction. 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," to express pride and conviction to stand up, rather than bow down, to 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 night 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."
Many went on Facebook and Twitter
to express their pride and conviction to stand up, rather than bow down, to terrorism.
"We are Indonesians & we never affraid to (sic) terrorist," one man wrote. "We always fight anything that wanna take us down."
This sentiment was echoed by President Joko Widodo.
"We should not be afraid and defeated by acts of terror like this," he said.
Chaos on a busy street
It began around 10:55 a.m. Thursday (10:55 p.m. ET Wednesday) with a suicide explosion near a Starbucks on Thamrin Street, an entertainment and shopping district with various Western chain restaurants and stores.
That set in motion two militants outside the coffee shop who seized two foreigners, dragged them into a parking lot and shot them, said Charliyan, the Jakarta police spokesman. They also opened fire at people on the street.
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.
First major attack in Jakarta since 2009
CNN security analyst Bob Baer likened the Jakarta attack to the November 13 Paris massacre in which terrorists linked to ISIS struck several locations at the same time.
Yet the number of dead was nowhere near the toll of 130 in France, with Clarke Jones, a counterterrorism expert at Australian National University, calling it "fairly amateurish ... with hand grenades and firearms."
It was the first major attack in Jakarta since the 2009 simultaneous attacks on the J.W. Marriott and Ritz Carlton hotels
, which left seven people dead. Since then, the secular government has made major inroads beating back terror groups in an Asian nation where about 87% of its roughly 255 million people are Muslim
"It's concerning (to have) yet one more day and another attack in another part of the world," Sajjan Gohel of the Asia-Pacific Foundation think tank told CNN. "And one fears that this is potentially becoming the new normal where ISIS affiliates carry out attacks independently from the leadership based in Syria."
Dutch national among the wounded
The blasts and gunshots stopped by Thursday afternoon. And by nighttime, authorities were no longer hunting for attackers -- though they are looking for those who helped them in plotting, financing and getting weaponry, Charliyan said.
By then, police had already counted five assailants dead at the scene. They also discovered several unexploded munitions, some of them high-grade explosives, at the scene, the police spokesman said.
One foreign national and one Indonesian make up the dead, authorities said. Charliyan said 24 people, including at least one more foreigner, were wounded.
The ISIS statement claimed "nearly 15 Crusader foreigners" died in the attack, though there are no official reports indicating that's true. The group said that its fighters "targeted a gathering of nationals of the Crusader alliance" -- suggesting they were going after not Indonesians but citizens of other countries, many of whom have a role in the far-reaching campaign against ISIS.
It added that the operation was intended to "teach the citizens of the Crusader alliance that it does not protect them" or guarantee them "safety in the Muslim lands."
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.
Worries about ISIS fighters returning home
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.