Indonesia is hunting for terror cells believed to be behind Thursday's attack that killed seven people, including two civilians, here, Jakarta's chief of police said.

Two civilians and five attackers died in the gun and bomb assault in a busy commercial district on Thursday, BBC reported.

Insp Gen Tito Karnavian said the attackers had been "neutralised" but were linked to groups across Indonesia and were "part of a global network".

The Islamic State (IS) militant earlier claimed responsibility of the attack. It released a statement online, saying it had been carried out by "soldiers of the Caliphate", targeting "citizens of the Crusader coalition" against the group.

Three men were arrested near Jakarta early on Friday, police told the media. It was not immediately clear whether they had direct links with the attacks.

Authorities have named Bahrum Naim, an Indonesian believed to be fighting with IS in Syria, as the suspected co-ordinator.

Security forces battled militants for hours on Thursday in a major business and shopping district of Jakarta, the report said.

The assault ended when two of the attackers were killed in a suicide bombing, said police, with the other three killed in gun battles.

A Canadian and an Indonesian national, both civilians, also died and at least 20 people were injured.