A police source said a bomb that exploded early on Tuesday outside the offices of Greece's industry association in Athens caused damage but no injuries.
The source added that calls 40 minutes before the explosion to two Greek newspapers at 00:50 GMT had warned the police beforehand making it possible for the police to clear the area before the attack against the Hellenic Federation of Enterprises (SEV) was committed.
The news reported that the caller left the message, "The bomb will explode in 40 minutes. This is not a hoax."
Although the police immediately considered a possible connection with an international terrorist group, the warning before the attack and the target chosen indicated it could have been a domestic far-left group.
Greek authorities say they had already taken strict precautions to provide further security after the Paris bomb attacks on November 13 which were claimed by DAESH, however, no one group has claimed responsibility for the blast so far.
According to footage shown on state TV, the explosion shattered windows and caused minor damage to a building which is near to one of Athens' top hotels as well as the Greek Cypriot embassy and EU offices.
The blast followed an arson attack against the house of a top minister on Saturday, in which assailants set fire to a cannister of gasoline.
A message posted on an anti-establishment website on Monday in relation to the arson attack said, "Politicians, you have no reason to sleep peacefully."
In July, Prime Minister Tsipras' leftist government agreed to an unpopular EU bailout to save Greece from being excluded from the euro.
The government was forced to legislate a new austerity policy and is about to reform Greece's pension system, which is expected to demand higher contributions.
In Greece, government buildings, business offices and banks are common targets for attacks by far-left groups, usually with the aim of causing damage without harming passers-by.
The SEV offices were attacked in also 2010 and responsibility for the attack was claimed by a far-left group named Zero Tolerance.