"We want to determine whether security procedures were followed," a police source told AFP, hours after Papademos and two guards were injured by the bomb that exploded as they rode in an armoured car in Athens.
"The fact that the attackers managed to get past security is worrying," the source said, adding that experts were trying to determine the nature of explosive used.
Papademos sustained superficial injuries to the chest, abdomen and legs, Evangelismos Hospital in Athens said, after he apparently opened his mail whilst riding in the car.
A later statement from Evangelismos Hospital said the former PM had undergone surgery to address a thigh injury.
One of his guards has trouble hearing, the hospital said.
The police source said the attack was "largely symbolic" as Papademos was lightly hurt despite his proximity to the letter bomb.
Calls have already gone out to individuals who could be potential targets to boost security, and to the Greek postal service to step up searches for other similar devices.
Leaders of all parties and former prime ministers condemned the attack, the first against an incumbent or former leader in decades.
The methodology is similar to that used by Conspiracy of Fire Nuclei, a domestic far-left group which in March mailed a letter bomb that injured a secretary at the International Monetary Fund in Paris.
The group had earlier claimed responsibility for an explosive device, also sent from Greece, discovered by the police at the offices of German Finance Minister Wolfgang Schaeuble.
The police source acknowledged that Thursday's attack on Papademos was "similar" to those in March, but authorities do not want to rule out other possibilities.
Papademos' name was on a target list compiled by Paula Roupa, a senior member of far-left group Revolutionary Struggle jailed in January.
So far there has been no claim of responsibility.
If Conspiracy does confirm the attack, "it would be a problem," the police source said.
"It would show that they have done their homework and are able to bypass security procedures," the source added.
In 2011, several Conspiracy members, many of whom were very young, were convicted of "participating in a criminal organisation" and given long prison sentences.
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