Greek media report that the gunman killed two men and a woman before turning the gun on himself.
The suspect was found dead next to a hunting rifle that was believed to have been used in the shooting. Police say the gunman was a former employee who had recently been fired. The owner of the company, European Product Carriers, was among the dead.
The incident, which initially prompted a hostage situation, happened in Glyfada, about 12km (7 miles) south of Athens.
The armed man broke into the building, shot at employees, and then killed two men and a woman before barricading himself inside.
A witness, identified as a company worker, told journalists outside the building: “I heard the gunshots, I heard the first two. I headed towards the stairs to see what was happening. I saw two guys coming down, they said, ‘It’s Aris with a gun, he’s shooting.’
“Of course, I dashed outside, towards the garden, and made my way out through the back door of the garage.”
Police cordoned off a large area around the building and the elite counter-terrorism unit EKAM, as well as fire engines and ambulances were stationed outside.
As the standoff continued, the gunman remained barricaded on the second floor of the building.
A police negotiator tried to defuse the situation for several hours but the man eventually turned the gun on himself.
The shooter has been identified as a 70-year-old Egyptian national.
Shootings – outside of gang-related activity – are rare in Greece, which has strict laws over gun possession.
Many Greek and foreign shipping companies have offices in Glyfada, a seaside resort to the south of Athens.
European Product Carriers owns an average fleet of 35 vessels including oil tankers.
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