A domestic militant group called Revolutionary Struggle has now entered the fray.
The proof, according to Greek officials, comes in the form of bullets fired during an attack on a riot police unit guarding the culture ministry in central Athens on Monday.
Ballistics tests revealed that one of the bullets came from the same weapon used in an attack on an Athens police station in April 2007.
Revolutionary Struggle, described as "a radical leftist group" in a recent US state department report on terrorism, said it had carried out that attack.
Previously, the group also claimed a rocket attack on the US embassy in Athens the same year.
A 21-year-old member of the riot police unit, Diamandis Mantzounis, is in a critical condition after the attack. He was shot in the body and leg - though the bullets that struck him were fired from a second weapon.
Greece's national police chief, Lt Gen Vassilis Tsiatouras, said that was a Kalashnikov, that tests showed was also used in an attack last month on a bus carrying 22 riot police.
However, the general attempted to play down a resurgence of domestic terrorism.
He said he thought the attacks were the work of a group of people who had "lost their senses" following the death of 15-year-old Alexis Grigoropoulos on 6 December 2008.
The shooting, by a 37-year-old policeman, triggered weeks of riots across the country.
History of terror
Monday's developments are regarded as highly significant by anti-terrorist specialists at the US embassy in Athens, who are analysing the "format, the fashion, and the weapons" used in the attack.
The embassy is still offering a $1m (£690,000) reward for information leading to the successful prosecution of the Revolutionary Struggle operatives, who fired a rocket-propelled grenade into the building in January 2007.
The state department said it believed the Revolutionary Struggle was also responsible for "nine violent terrorist attacks since 2003, including the 2004 murder of a Greek guard outside the British defence attache's residence".
It said that in 2006, the group claimed responsibility for triggering a remote-controlled explosive device targeting the Greek culture minister.
The big question troubling Greece is whether there is going to be a revival of domestic terrorism along the lines of November 17 (N17), another "populist" left-wing anti-capitalist group, responsible for two dozen assassinations and scores of bomb attacks during a three-decade campaign.
The Greek authorities disbanded N17 after Savvas Xeros, a painter and son of an Orthodox priest, was caught in 2002 when the bomb he was planting exploded prematurely.
The involvement of British detectives, following N17's murder of the UK's defence attache, Stephen Saunders, in 2000, also helped the Greek police bring the case to trial.
Fifteen members of N17 were given lengthy jail sentences.
Flash in the pan?
The US state department says the Revolutionary Struggle has "aligned itself with the ideology of N17" and may have incorporated some of its former members.
However, Brady Kiesling, a former US embassy diplomat in Athens told the BBC: "Revolutionary Struggle are people inspired by N17, but the organisation is not a successor except vaguely psychologically.
"What you have are spontaneous, arbitrary attacks. When there is a political window, they will mount an attack - without the level of preparation that N17 used."
He said: "They are dangerous, but not nearly as dangerous as N17 were.
"N17 was massively security conscious. They lived off the land. They never indebted themselves to anybody. It sounds as though Revolutionary Struggle is buying from the illegal arms market, such as the Albanian dealers. N17 would never do that."
Mr Kiesling said advances in DNA analysis, security surveillance and mobile phone analysis made it much harder to do what N17 used to.
"My gut tells me this is a flash in the pan," said Mr Kiesling, who is writing a book about N17.
"Most of the far-left groups out there prefer a live-and-let-live approach with the police. This kind of shooting destabilises the status quo. There will not be a lot of social support for the shooting."
That will not come as much relief to the average policeman on the street, who has become a hate figure for much of the population.
Last month, a young police officer called Jimmy contacted me because he was weary of the Greek media demonising the force, and wanted to "put the record straight".
"Not every Greek policeman is a batsos!" Jimmy implored.
"Batsos" forms the first word of the derogatory chant directed at the police at every opportunity by Greek demonstrators.
The media interprets the phrase as "cops, pigs, murderers".
But batsos is much more derogatory than just "cop".
The word comes from the verb to slap and, to use a euphemistic translation, it means "uniformed thug".
The insult was particularly popular from 1967-1974, when Greece was ruled by a harsh military junta, and police violence was commonplace.
Jimmy says he and his colleagues have been advised not to wear their uniforms when travelling to and from work.
"We are afraid that one of us will be murdered soon," he says.
As Monday's shooting outside the culture ministry proved, the young officer's fears had a solid foundation.
"I don't believe this hatred of the police is justified. I always try not to use violence and use respect when I arrest someone," Jimmy said.
"But at the moment, my colleagues and I are tired of adopting a defensive posture."
The latest shooting may change all that.Says Brady Kiesling: "This licenses police to arrest people again. They are angry enough to take more risks."