Indonesian police killed one suspected militant and arrested two more in raids across the country, a day after an attack by Islamic State suicide bombers and gunmen in the heart of the Southeast Asian nation's capital.

Seven people were killed in Thursday's late-morning siege near a busy shopping district, despite multiple blasts and a gunfight, and five of the dead were the attackers themselves.

Nevertheless, it was the first time the radical group had targeted the country with the world's largest Muslim population, and the brazenness of the attack suggested a new brand of militancy in a country more used to low-level strikes on police.

Police chiefs across the country were on high alert, some embassies in Jakarta were closed for the day and security was stepped up on the resort island of Bali, a draw for tourists from Australia and other Asian countries.

"It's clear that the [Jakarta attackers] didn't set this up themselves. For this, we are searching for the networks and who was involved in this action," said Anton Charliyan, national police spokesman.

Security forces killed one suspected militant in a gun battle in Central Sulawesi, while two others were arrested in the city of Cirebon in West Java.

The three were believed to be Islamic State supporters, but not directly connected to the Jakarta attack, police said.

Returning to the area outside Jakarta's oldest department store, Sarinah, where Thursday's attack unfolded, the city's police chief said the rise of Islamic State was a cause for serious concern.

"We need to strengthen our response and preventive measures, including legislation to prevent them ... and we hope our counterparts in other countries can work together because it is not home-grown terrorism, it is part of the ISIS network," Tito Karnavian said, using an acronym for the Syria-based group.