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Nikos Maziotis was charged in 2010 over a series of attacks claimed by the Revolutionary Struggle group, including firing a rocket propelled grenade at the U.S. embassy in Athens in 2007 and a 2009 car bomb that damaged the Athens stock exchange.
"His arrest is undoubtedly a very big success," Public Order Minister Vassilis Kikilias told a news conference broadcast live on Greek television.
Maziotis had been on the run since 2012. Anti-terrorism police had deployed agents in places he was believed to frequent and he was spotted as he was entering an outdoor equipment shop in central Athens, police said.
Maziotis, 42, was eventually caught in the city's shopping district after a chase through three crowded blocks in the tourist area of Monastiraki at the foot of the Acropolis.
He fired eight times at the policemen chasing him and received one shot back, police chief Dimitrios Tsaknakis said.
Media showed a photograph of Maziotis - who was wearing a wig and carried a fake ID when arrested - lying on the ground, drenched in blood and handcuffed.
He was shot in the shoulder and underwent surgery at an Athens hospital but his life is not in danger, Health Minister Makis Voridis told reporters.
A policeman was injured in the leg during the shootout, Voridis said. A 19-year-old Australian tourist sitting in a nearby restaurant was injured by a bullet splinter in his ankle and a German tourist was lightly hurt, but not hospitalised.
Police were looking for a second suspect, a police official told Reuters, declining to be named.
After spending the maximum period of 18 months in pre-trial detention, Maziotis was released in 2012 with orders to regularly appear at a police station until his trial concluded.
But after the trial began, Maziotis went on the run with his partner, also a member of the Revolutionary Struggle. In 2013 the two were sentenced to jail in absentia. In January, authorities offered 1 million euros ($1.35 million) for help in his capture.
Revolutionary Struggle was set up in 2003 and declared war on all forms of government. It later said it was protesting against austerity measures imposed during Greece's financial crisis that forced thousands out of work and plunged the economy into a deep recession.
The group had been considered dismantled in 2010, but in April it claimed a car bombing at a central bank building, which came hours before Greece tapped bond markets for the first time since its EU/IMF bailout began four years ago.
The group said the attack was a protest against Greece's return to bond markets. There were no injuries.