Greece, Italy, Spain, Syria, and Turkey were the top olive oil producing countries in 2001 / 2002 – but with quite some differences between their respective outputs:
Season ending in 2002
Greece 358,500 tons
Italy 656,500 tons
Spain 1,411,500 tons
Syria 92,000 tons
Turkey 65,000 tons
Source: www.olivenoel-info.de
Just to give you an idea as to how volatile the outputs per country were during years from 1999 to 2003, here is a graph of three European countries:

EU Countries Olive Oil Production per Year
In autumn 2007, fires in Greece led to substantial losses in the country’s olive oil production. Given that it takes an olive tree some seven years to grow before it becomes productive, Syrian producers, expecting a record harvest, hoped for rising prices all the same.

Olive Grove northeastern Syria
(The trees are skillfully bred – Jesus had to wait longer than for seven years.)
In 2007, the numbers were as follows:
Greece 394,700 tons
Italy 590,000 tons
Spain 1,326,000 tons
Syria 152,000 tons
Turkey 172,000 tons
Source: Wikipedia (German)
Syria, one of the first sites of olive trees, had increased its production substantially.
In northeastern Syria, the groves are not only in the plains. Places which are less easy to farm are also used, as labour is cheap here, and no half-automated farming is needed. A good share of the oil is used for the production of Aleppo soap. The soap producers in and around the city of Aleppo usually use the second pressing out of the olives.
According to Wikipedia (German), the 2007 ranking list of oil-producing countries (in order of their output, from biggest to smallest, reads Spain, Italy, Greece, Tunisia, Turkey, Syria, Morocco, Algeria, Portugal, Libya, Palestinean territories (Gaza Strip, West Bank), Argentina, Jordan, Egypt, and Lebanon. Combined, they produced 3,107,493 tons or 99.2% of the global olive oil output. EU countries alone account for 75.8% of global olive oil production.
Tags: Aleppo, Alepposeife, EU, Europe, farming, history, Italy, olive oil, Palestine, Syria, trade