Police alleged one - Afif Sunakim, apparent accustomed a gun and haversack during the attacks. He was accustomed a seven-year bastille appellation for accessory a active camp.
All 5 died in Thursday's attacks, which larboard two civilians asleep and were claimed by Islamic State (IS).
Three arrests were fabricated on Friday but it is cryptic if they are connected.
Security armament battled militants for hours in the active bartering commune area the militants struck.
A Canadian and an Indonesian civic died, and at atomic 20 humans were injured.
The advance concluded if two attackers died in a suicide bombing, badge say, with the added three dead in gun battles.
Following contempo IS threats, the country, which had been attacked by Islamist militants several times in the past, had been on top alert.
Gen Badrodin Haiti, the civic badge chief, said Sunakim and one added antagonist had both been bedevilled criminals.
Jakarta's arch of police, Insp Gen Tito Karnavian, said a coursing was beneath way for alarm beef believed to be abaft the attack.
Three men were arrested abreast Jakarta aboriginal on Friday, badge told bounded media.
A badge spokesman, Anton Charliyan, accepted on Friday that those who organised the attacks were associated with IS.
Two of the perpetrators, he added, were "known to accept committed agnate abolitionist activities some time ago".
Earlier, Bahrum Naim, an Indonesian believed to be angry with IS in Syria, was alleged as the doubtable co-ordinator.
Insp Gen Karnavian said Naim's "vision" was to affiliate assorted IS-supporting groups beyond South East Asia.
IS appear a account adage it had targeted citizens of countries which are allotment of the all-embracing affiliation angry the group, which controls locations of Syria and Iraq.
'Game-changer' for Indonesia - Ali Moore, BBC News, Jakarta
Life is accepting aback to accustomed on the alliance area the advance happened - but alone up to a point.
Traffic is abounding and the alley sweepers are active but the badge column which was hit charcoal boarded up, and the Starbucks bistro at the centre of the advance is amidst by adamant fencing, analytical assemblage and media application annihilation at duke to associate over the top at the destroyed out windows.
The comfort flowers accept now been removed - apparently to stop the crowds acquisition to yield selfies, risking their lives in the morning traffic.
But with the city's badge arch acceptance Thursday's advance is acceptable to be a game-changer for Indonesia, there is no agnosticism the accident of addition advance has taken a new form. And no amount how "tiny" the group, as he alleged them, they accept accepted they can kill.
Insp Gen Karnavian told the BBC the capital culprits were "connected to added beef in Java and Sulawesi and we are block them".
He said one IS artifice had been aghast at the end of 2015 and a amount of humans detained, a allotment of them a man who said he had been instructed by Naim.
Naim has been affiliated to the IS-allied East Indonesia Mujahidin Accumulation (MIT), which is based on the island of Sulawesi.
Insp Gen Karnavian said Indonesia had decidedly developed its compassionate of calm active networks back the 2002 bomb advance in Bali, which dead 202 people.
Some 1,000 humans affiliated to abolitionist networks had been brought to amends in Indonesia back 2000, he said, but some had back been appear from bastille and had "the abeyant to affectation a threat".
"What we charge to do today is strengthen adequacy and aswell administration advice with others because it is not home developed in Indonesia but it is allotment of a all-around network," he said.
Indonesian President Joko Widodo tweeted on Friday that there was "no abode for agitation on Earth" and that "every aborigine in the world" bare to action it.
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