At least two Australians were injured in the series of coordinated attacks that killed nearly 80 people as heavily armed Islamist militants hit two luxury hotels and took foreign guests hostage.

"This is a cowardly act. It's indiscriminate, it's a terrorist act, it's an assault on democracy," acting Foreign Minister Simon Crean told a news conference.

A group calling itself the "Deccan Mujahedeen" claimed responsibility for the assaults on the landmark Taj Mahal and Trident hotels and a number of shooting and bombing incidents elsewhere in the city.

The attacks drew condemnation worldwide, with Washington calling them "horrific", while US president-elect Barack Obama pledged to work with India to "root out and destroy terrorist networks."

Britain's Prime Minister Gordon Brown said the "outrageous" attacks in its former colony would be met with a "vigorous response", and the European Union expressed its "horror and indignation" at the violence.