At least seven people are dead after militants launched an assault on the Indonesian capital Jakarta, in a series of bomb blasts and gunfire, police have said.

There were several large explosions across the city - with reports that at least three suicide bombers targeted multiple locations, including a Starbucks cafe at a busy shopping centre near the presidential palace.

Three other blasts were reportedly heard in the Cikini, Silpi and Kuningan neighbourhoods, near the Pakistan and Turkish embassies.

Police said a gun battle with attackers also took place inside a cinema at the retail complex.

Bodies could be seen in the streets, as office workers watched the horror unfold from high-rise buildings.

Footage showed two suicide bombers blow themselves up outside the cafe, and a militant was also believed to have been captured on film exchanging gunfire with police.

Tri Seranto, a security guard at a bank, said he saw at least five attackers, three of them suicide bombers, who entered the cafe and blew themselves up, one by one.

However, police said it was unclear if they detonated themselves or hand grenades.

Security forces stormed the building, and gunfire could be heard more than an hour after the explosions.

Mr Seranto said the two other attackers, who were carrying handguns, entered a nearby police post from where he heard gunfire.

Police said seven people, including five attackers, were dead.

It was unclear how many of the attackers were shot dead or blew themselves up.

Two civilians died in the attacks, and there were conflicting reports a foreign national was either among those injured or killed.

Officers have arrested four people suspected of being involved in the assault, and said no assailants had escaped.

A Reuters photographer said: "The Starbucks cafe windows are blown out. I see three dead people on the road".

"There has been a lull in the shooting but someone is on the roof of the building and police are aiming their guns at him".

No one has claimed responsibility for the attack, but police said terror group Islamic State had issued a cryptic warning before the assault, saying, "there will be a concert in Indonesia and it will be international news".

Starbucks said one customer was injured and treated at the scene, and confirmed all its employees were safe and that it was closing all its branches in the city until further notice.

"We are deeply saddened by the senseless acts that have taken place in Jakarta today; our hearts are with the people of Indonesia," the firm said in a statement.

We are deeply saddened by the tragic acts that have taken place in Jakarta today.

— Starbucks Indonesia (@SbuxIndonesia) January 14, 2016

A United Nations building close to the scene was in lockdown, and other high-rise buildings in the area have been evacuated.

Indonesian President Joko Widodo condemned the assault as "acts of terror" and urged people to remain calm.

He said: "Our nation and our people should not be afraid, we will not be defeated by these acts of terror, I hope the public stay calm".

Indonesia has been a victim of several bombings in the past that have been claimed by Islamic militant groups.

The country has been on high alert since authorities said they foiled a plot by Islamic militants to attack government officials, foreigners and others.

Around 150,000 police officers and soldiers were deployed on New Year's Eve to protect churches, airports and other public places.