So-called Islamic State has claimed responsibility for the Jakarta attacks, which were "targeting foreign nationals and security forces".
The announcement was made on an IS-allied news agency.
The police chief in the Indonesian capital has also said the group is "definitely" behind the attack.
An eyewitness to the Jakarta attacks has described panic in the streets following the first explosions.
Australian Andrew Gadd, who works in the Indonesia capital, told ITV News he heard a loud bang while in his office and then someone began shouting "bomb, bomb, bomb".
He said when he looked out of a window he saw another explosion and people running in the street.
"You could see people running away and ducking and hiding behind cars," said Mr Gadd.
ITV News Security Editor Rohit Kachroo tweets:
Indonesian authorities had expected an attack: 150,000 security personnel deployed, arrests made, talk of 'credible threat' over recent wks
Authorities say Jakarta attackers imitated the Paris terrorists. Assumption perhaps. But they can't yet say for sure whether IS responsible
Before Xmas, Australians Attorney-General said IS wanted a 'distant caliphate' in Indonesia.... Great deal of skepticism about comments
Few hundred Indonesians have gone to Syria to join IS/other groups - perhaps 500. Many more Brits are thought to have gone
Figures suggest Indonesian authorities have been relatively successful in combatting draw of extremism - relative to UK for one
Militants who attacked a busy shopping area in downtown Jakarta were copying the Paris attacks, authorities have said.
Indonesia's national police spokesman also said they probably had connections to so-called Islamic State.
General Anton Charliyan said: "They imitated the terror actions in Paris...they are likely from the (Islamic State) group."
Indonesian police have arrested four suspected militants following the gun and bomb attacks in the centre of the capital Jakarta.
Five assailants were confirmed dead, along with two other people.
Police declared the area secure shortly before 8am GMT after sweeping through the area.
Jakarta police spokesman Col. Muhammad Iqbal said: "We believe there are no more attackers around Sarinah. We have taken control."
Militants have launched a series of co-ordinated bomb and gun attacks in the Indonesian capital Jakarta. Here's what we know so far.Read the full story ›
Surveillance footage has emerged showing an explosion outside a Starbucks in central Jakarta.
The area around the explosion appeared quiet, with no pedestrians in sight.
This video being shared on social media appears to show people fleeing amid heavy gunfire in the Indonesian capital Jakarta.
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Starbucks has said it is "deeply saddened by the senseless acts" in Jakarta.
The company said one customer was injured and treated at the scene, with all employees confirmed safe.
"Our hearts are with the people of Indonesia," the company said in a statement.
"Amidst reports of attacks targeting police posts throughout central Jakarta, initial reports are that an explosion took place close to our store in the Skyline building near one of these police posts.
"This store and all other Starbucks stores in Jakarta will remain closed, out of an abundance of caution, until further notice."
Twitter members in Indonesia have begun using the hashtag #KamiTidakTakut, meaning "We Are Not Afraid", following the deadly attacks in the capital.
Several people have been killed in a series of co-ordinated bomb and gun attacks in Jakarta.