By Ahmad Pathoni

Jakarta (dpa) - In what the European Union called a "tragic reminder" of a global phenomenon, seven people - including five suspected attackers - died in bomb blasts and gunfire in the centre of the Indonesian capital Jakarta on Thursday, officials said.

The assailants struck outside a Starbucks cafe and a police post near the well-known Sarinah shopping complex, police said.

Jakarta police chief Tito Karnavian said the group behind the attacks "has links with Islamic State."

"They used to operate only in Syria and Iraq, but now they have cells in South-East Asia, including in Indonesia," he said.

Islamic State claimed responsiblity for the attack, the militia's news agency al-Amaq said in a post on social media.

"A platoon of the Caliphate soldiers in Indonesia targeted in Jakarta a crowd of citizens from the Zionist alliance that fights Islamic State," the statement said.

The post claimed that at least four gunmen - using bombs timed to explode as they attacked with light weapons and explosive belts - killed at least 15 people.

The authenticity of the post could not be verified independently.

City police spokesman Muhammad Iqbal said two of the attackers blew themselves up while the other three were killed in a gunfight with police.

State Secretary Pramono Anung told reporters that one of the two bystanders killed was a Canadian national.

Twenty people were injured, including five police, Pramono said.

Police said they believed no attackers were on the loose.

Starbucks said one of its customers was injured in the attacks, but that its employees were unhurt.

President Joko Widodo called for calm.

"We must not be afraid and be defeated by this terror act," Joko was quoted as saying by Kompas.com news website.

Soon after the attack started, police cordoned off the area, which contains many offices, and using loudspeakers told people to remain in their buildings. Later hundreds of police and soldiers arrived in armoured vehicles.

The busy district is home to United Nations offices and the French embassy, but there appeared to be no serious damage from the blasts to larger buildings in the area.

"I was in a meeting when I heard an explosion and then there was gunfire," said Ruly Koestaman, an office worker in a nearby building.

"We went down and saw three people lying dead, and also two foreigners badly injured but still alive," he said.

European Union foreign policy chief Federica Mogherini said the attack was "tragic reminder that the threat of terrorism is global and has to be tackled globally."

"Our hearts go out to the families and friends of the victims," she said. "We stand firm by the Indonesian government and its people in their fight against violence and extremism."

A video broadcast by TVOne showed one of the attackers igniting an explosive, killing himself and an apparent accomplice behind him while they were ducking for cover behind a car during a gunfight with police.

Television footage showed a handgun, three home-made granades and a knife recovered from the dead attackers.

An earlier rumour that blasts went off in three other Jakarta locations proved untrue, TVOne said.

Indonesia has faced problems in recent years with extremist violence, often linked to Islamist groups, and it is estimated that hundreds of Indonesians have joined the Islamic State group in the Middle East.

Police last month arrested nine suspected militants they said were planning coordinated attacks on New Year's Eve.