Some companies doing business at the Olympic Games were still looking for terrorism cover this week, according to Marsh.
"There are still people looking at terrorism protection," said Marsh senior broking director James Hopper.
Hopper said underwriters were still receiving enquiries about terror cover just days before the launch of the games in Athens.
He warned that rates for cover could be set to increase this week as market capacity gets tighter.
"We've been placing [Olympic] cover since before 9/11 - rates have tripled since then but they could get higher as there's a capacity crunch."
But Hopper added that some companies may forego terrorism cover after seeing that security at the games will be much stricter than at first thought.