They claimed responsibility for a similar letter bomb sent in March, which wounded a woman as she opened it at the offices of the International Monetary Fund in Germany.
Mr. Papademos, who was governor of the Bank of Greece from 1994 to 2002 and vice president of the European Central Bank from 2002 to 2010, was taken to hospital with chest, stomach and leg injuries after the attack on Thursday, May 25.
But he is now out of danger. Two Bank of Greece employees who were in the car with the 69-year-old were also wounded.
Mr. Papademos became a hate figure for many on the left and on the extreme right when his government signed a memorandum of understanding with the European Union in March 2012.
In return for a 130 billion euro (US$145 billion) bailout, Papademos's government agreed to a series of austerity measures which cut deep into the fabric of Greek society.
There were riots in the streets of Athens and Papademos was demonized by the anti-austerity movement, especially the Syriza party, led by Alexis Tsipras, the current prime minister.
Tsipras tweeted on Thursday:
Καταδικάζω απερίφραστα την επίθεση ενάντια στον Λουκά Παπαδήμο. Εύχομαι ταχεία ανάρρωση στον ίδιο και τους ανθρώπους που τον συνόδευαν.— Prime Minister GR (@PrimeministerGR) May 25, 2017
Tweet: "I strongly condemn the attack on Lucas Papademos. I wish a speedy recovery to him and the people who accompanied him."
Greek newspaper columnist Paschos Mandravelis said Syriza had accused Papademos of being the leader of a "junta" because he had never been elected and was the head of a provisional government set up in November 2011 after the collapse of George Papandreou's Socialist administration.
"There was a lot of hatred directed towards him and this hatred has grown and terrorists have found a way to get to him and try to hurt him. Tsipras has condemned it now but he fueled the rhetoric," Mr. Mandravelis told Sputnik.
Mr. Mandravelis, who lived through the rule of the Greek colonels between 1967 and 1974, said:
"This rhetorical hatred was spread among the young people and many of them called it a dictatorship. They do not understand the difference between a democracy and a dictatorship."
He said both political extremes compared Mr. Papademos and members of his government with those who had collaborated with the Nazis during the war.
Greece has a history of terrorism, most notably the November 17 group, who named themselves after a date in 1973 when 20 students were killed when they rose up against the military junta, known as The Colonels, who ruled Greece at the time.
They carried out a number of assassinations and bombing during the 1980s and 1990s and in 2000 killed British defense attache Stephen Saunders in Athens.
But Alexandros Giotopoulos, 59, Dimitris Koufodinas, 46, and several other key members of November 17 were jailed for life in 2003, when the group was smashed.
"November 17 were terrorists but they had some political thinking. These new groups are from a younger generation and they think they are in an action movie. Their names are so spectacular."
"These people are using names that come from Hollywood, not politics," Mr. Mandravelis said.
The phrase the Conspiracy of Cells of Fire was coined by Theofolos Mavropoulos in a document that can be found online in the Anarchist Library.
Dr. Bones, a US-based journalist who has written about the CCF, said: "The CCF are not terrorists but revolutionaries, anarchists who have had enough of simply watching capitalism destroy human lives.
"This is class war beyond mere slogans, beyond protest signs, and made a reality. Greeks I know have cheered the action and hailed it as a strike against the powerful in the name of the exploited," he told Sputnik.
"They are more akin to the IRA than ISIS [Daesh]. They're fighting for their own liberation and the destruction of all that destroys the human spirit," he told Sputnik.
Antonis Samaras, who succeeded Mr. Papademos as prime minister, said on Thursday night: "The letter arrived at his home after undergoing checks which did not detect the explosive material."
All were intercepted, although in the case of the package sent to the IMF a female employee was wounded as she opened the parcel in March.
Greece's economy remains in dire straits and Mr. Tsipras said last month the Greek parliament would only vote on further economic reforms in 2019 only after measures to solve the problem of state debt in the country are adopted and implemented.