The unexpected offer was made in a telephone call from Hilton's chief executive officer, Stephen Bollenbach, to the management of ITT yesterday.
Hilton would expect to assume about $4bn in debt to conclude the buyout; the transaction would thus be worth a total of $10.5bn.
"The combination of ITT and Hilton would bring together two of the world's leading lodging companies as well as two premier gaming businesses," Mr Bollenbach said in a statement last night.
Eighteen months ago ITT undertook a giant demerger, separating its hospitality divisions from its other businesses such as insurance.
The new ITT that emerged, and which is now in Hilton's sights, includes Sheraton, the Caesar's World casinos chain and the Madison Square Garden arena in New York as well as New York sporting teams the Knicks and the Rangers.
Hilton said it was offering to buy all outstanding ITT shares.
It would pay $55 a share in in a two-phase transaction, in cash for the first half of the tender followed by a secondary offer worth the same amount paid for with Hilton common stock.
In a written bid, it indicated that it was also seeking an early meeting of ITT shareholders to vote on replacing its board of directors.
There was no immediate comment from ITT last night. For shareholders, however, it may be hard to resist.
The Hilton offer price would represent a 29 per cent premium on the current price of ITT shares, which closed last night off $1.125 at $42.625.
A combination of the two companies would result, meanwhile, in a hotel and gaming behemoth.
The Hilton group comprises 240 hotels with 100,000 rooms. It additionally operates 16 casinos, including the famed Flamingo in Las Vegas.
ITT has 415 hotels with 130,000 rooms and a collection of 14 casinos across the United States.
Hilton said that through a merger, it would be in a position to cut operating costs of the combined company by $100m a year.