Loss adjusters Crawford & Co expect the US terrorist attacks to be the most expensive insured man-made disaster in history.
The company added its reckoning, of losses in the billions of dollars, to a growing number of estimates.
It has mobilised its biggest ever international loss team and will bring in experts from all over the world.
They expect to get access to the site, including where the World Trade Center stood until its destruction by hijacked passenger jets on Tuesday, within the next few days.
The company's staff and offices in New York were unaffected.