The following is a fact file on the background and activities of the elusive outfit, which is known for its letter bombs.
Who are they?
Police say they are militant youths with no proven links to other Greek extremist organisations.
In contrast to other groups who have used industrial explosives and assault weaponry, Conspiracy tends to use common materials in their attacks such as gas cannisters, gunpowder extracted from firecrackers, and pressure cookers.
The organisation denounces capitalism, consumerism, police repression and worker exploitation.
Police say the name "Conspiracy of Fire Nuclei" has been used as cover by urban militants carrying out minor arson attacks against car dealerships and police vehicles since the middle of the last decade. But their activities escalated from early 2008 onwards.
How do they operate?
The group aims for maximum effect with minimum risk. In January 2008 they carried out a late-night arson barrage against Athens luxury car dealerships and banks. Nobody was injured.
At the time, gas cannister bombs were their weapon of choice, but the outfit quickly upgraded to explosives hidden in pressure cookers as well as dossiers and carved-out books.
In most cases, anonymous telephone calls were used to alert authorities before the explosives went off.
The device found at the Paris offices of the International Monetary Fund (IMF) where the letter bomb exploded appeared "to have been a firework or a big firecracker, according to the city's police chief, who described the device as "relatively rudimentary and nothing like a bomb".
The group began to be taken more seriously by police in February 2009 after planting a gas cannister bomb outside the home of a senior prosecutor. It caused minor damage.
In July 2009, another bomb hidden in a pressure cooker detonated outside the home of Greece's former police minister and in early 2010, it targeted the Greek parliament. Nobody was hurt in either incident.
In late 2010, the group began to expand their range of targets, sending a series of letter bombs to European leaders including Angela Merkel, Nicolas Sarkozy, Silvio Berlusconi and Jose Manuel Barroso, the then-president of the European Commission. Again, there were no victims.
Brush with police and resurgence
In 2011, several of its members, many of whom were very young, were convicted of "participating in a criminal organisation" and given long sentences in prison.
But three years later the group announced its return and has since committed sporadic attacks, including on the headquarters of the Greek socialist party PASOK, who at that time were sharing power with the right-wing New Democracy.
Many Greeks blame Germany and the IMF for imposing years of public sector cuts and reforms in exchange for bailout packages needed to prop up the debt-ridden country.