While no group claimed responsibility for the blast, many past bombings have been claimed by anarchist groups and Chile's government said it would invoke the country's tough anti-terror laws.
The explosion took place during lunchtime at a restaurant in a small, underground shopping mall connected to the Escuela Militar subway station in Santiago's affluent Las Condes neighbourhood yesterday.
Witnesses described a gory and chaotic scene as the blast sent bodies flying, while commuters ran away from the smoke screaming.
"That's why we're going to use the full force of justice, including invoking the anti-terrorist law," Bachelet said.
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The anti-terror law enacted during Chile's 1973-90 dictatorship lets suspects be held in isolation without charges and permits the use of phone taps and secret witnesses in investigations.
At least 14 people were injured in yesterday's attack, according to a list released by local hospitals. The government's emergency medical service said that among those hurt in the blast was a cleaning woman who lost a finger.
In some cases anarchist groups have said the bombs were planted to demand freedom for two Chilean anarchists imprisoned in Spain for an explosion in a cathedral in Zaragoza last year.
In yesterday's blast, the injuries apparently were caused by fragments from a fire extinguisher filled with gunpowder that detonated in a trash bin, said fire department Commander Ivo Zuvic Garcia.