Police said four of the attackers and three others were killed in the brazen attacks, which came after several warnings in recent weeks by the police that Islamic militants were planning something big. It was unclear if other perpetrators remained at large.
No one has claimed responsibility for the attacks but suspicion is likely to fall on Islamic militant groups, which have carried out several attacks in the past across Indonesia, the world's most populous Muslim nation.
It would be the first major attack in the capital Jakarta since the bombings of two hotels in 2009.
“This act is clearly aimed at disturbing public order and spreading terror among people,” President Joko Widodo, said in statement on television. Mr Widodo who is on a working visit in West Java town of Cirebon, said he is returning to Jakarta immediately.
“The state, the nation and the people should not be afraid of, and lose to, such terror acts,” he said.
The first explosion apparently triggered a gun-battle between the attackers and anti-terror police squads, and gunfire could be heard more than 1 1/2 hours later.
Tri Seranto, a bank security guard, told The Associated Press he saw at least five attackers, including three suicide bombers who exploded themselves in the Starbucks.
He said he was out on the street when he saw the three men entering Starbucks and saw them blowing themselves up one by one. He said the other two attackers, carrying handguns, entered a police post from where he heard gunfire. He said he later saw one policeman dead and three seriously wounded.
He said he was not injured in the explosions as he was a little distance away, but close enough to witness the attack at 9:30am Bangkok time.
He said the two gunmen ran away with police chasing them.
About two hours later, another explosion was heard from a cafe near the Starbucks, about five minutes after 25 anti-terror policemen entered it. It was not clear if the explosion was a controlled detonation or a bomb.
Gunshots were heard after the mid-morning explosion in front of the Sarinah shopping mall and a police station. The area also has many luxury hotels, and offices and embassies, including the French.
Tweets from the account of Jeremy Douglas, regional representative of the United Nations Office on Drugs and Crime for Southeast Asia and the Pacific, described a bomb and “serious” exchanges of gunfire on the street outside his Jakarta office. “Didn't experience this in 3.5 years in Pakistan,” he wrote.
About 30 minutes after his first post about the bombing, he posted that things were “quiet. Not comfortable quiet.”
Indonesia has been a victim of several bombing attacks in the past, claimed by Islamic militant groups.
Last month, anti-terror police arrested nine men and said the group had wanted to “perform a ‘concert’ to attract international news coverage of their existence here.” Police cited a document seized from the group that described the planned attacks as a “concert”.
The country has been on high alert after authorities said they had foiled a plot by Islamic militants to attack government officials, foreigners and others. About 150,000 police officers and soldiers were deployed during New Year’s Eve to guard churches, airports and other public places.
More than 9,000 police were also deployed in Bali, the site of Indonesia’s deadliest terror attack, which killed 202 people in 2002.
National Police spokesman Maj Gen Anton Charliyan said security is focused on anticipating attacks in vulnerable regions, including Jakarta.
On Tuesday, the jailed radical Islamic cleric Abu Bakar Bashir appealed to an Indonesia court to have his conviction for funding a terror training camp overturned, arguing that his support for the camp was an act of worship.
The 77-year-old leader of the Jemaah Islamiyah militant network filed a judicial review of his 2011 conviction, when he was sentenced to 15 years in jail for setting up the camp in Aceh province. A higher court later cut the sentence to nine years.
Indonesia has suffered a spate of deadly attacks by the Jemaah Islamiyah network in the past. But strikes in recent years have been smaller and less deadly, and have targeted government authorities, mainly police and anti-terrorism forces.
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