While there is a news blackout on the operation, codenamed "Hercules Shield", Greek military sources said U.S. forces would mainly play a command and control role for 2,000 Greek troops.
Practice scenarios that would be played out ranged from a so-called home-made nuclear "dirty bomb" to a ship hijack.
Far left groups and anarchists plan a demonstration at the U.S. embassy later on Wednesday to protest American involvement.
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In naming a new cabinet after sweeping socialists from power in a Sunday election, Karamanlis took personal control of the ministry responsible for Olympic preparations.
He appointed former Greek commando Giorgos Voulgarakis head of the ministry in charge of security and named civil engineer Giorgos Souflias to run the public works ministry responsible for major building projects like transport.
He chose as defence minister Spilios Spiliotopoulos, who as the shadow minister in opposition often accused the socialists of receiving kickbacks in return for defence contracts.
MUSIC TO EARS OF IOC
By taking over the Culture Ministry which supervises the Games, Karamanlis in effect did away with a whole level of decision-making that Gianna Angelopoulos, Athens Organising Committee chief, believed was a main obstacle to preparations.
The actions were music to ears of some worried International Olympic Committee officials who while maintaining an air of confidence in public that the Games would be ready, in private had run out of patience with the pace of preparations.
More than half of venues are still not ready including the main stadium, aquatic centre and the landmark marathon route.
In contrast, all venues were ready a year ahead of the Sydney 2000 Games and Beijing has promised its venue construction will be done two years ahead of the 2008 Games.
There are also serious delays in getting ready new transport routes like subways and trains, crucial for conducting Games in a capital notorious for its congested traffic.
There are major knock-on effects for the safety of the Games from the failure to get venues and transport ready.
Although Greece is spending three times as much on security as Sydney because of fear of international terrorists since the September 11 2001 attacks on U.S. cities, vital communications equipment cannot be installed and tested until venues are ready.
As part of its record 650-million-euro ($791.8-million) security plan, Greece has set up a seven-nation advisory group, comprising Britain, the United States, Israel, Australia, Spain, France and Germany. Russia and Turkey are also helping.
The two-week-long operation codenamed "Hercules Shield" that started on Wednesday will stretch from the southern Greek island of Crete to Athens.
It will take in the cities of Thessaloniki, Volos, and Patras, where football matches will be played, and the ancient birthplace of the Games in Olympia where the Olympic Flame will be lit on March 25 and where the shotput event will be held.
Sharing volatile land borders with Balkan nations like Albania and seas with Muslim nation Turkey, Greece is a nightmare for security planners.
Chief police spokesman Colonel Lefteris Economou, told Reuters only a global effort could protect the Games.
"If you want to tackle international terrorism, it can only be achieved through international collaboration," Economou said.
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