War of the Worlds took $34.6m (£19.5m) on its opening day, making it the most successful first day of a Tom Cruise film, according to studio estimates.
Paramount Pictures said Steven Spielberg's sci-fi thriller took $21.2m (£11.9m) in the US market alone.
By comparison, the final Lord of the Rings film took $57.6m (£32.6m) globally on its debut in 2003.
War of the Worlds, which has received largely positive reviews, is released in the UK on Friday.
The movie is based on British author HG Wells' book, which he wrote in 1898.
It was first turned into a movie in 1953, winning an Oscar for its special effects.
Although the US Independence Day Weekend is traditionally a lucrative one for the box office, there are doubts even the War of the Worlds release will be able to lift the industry out of its slump.
Revenue has declined for 18 straight weeks, compared with 2004's figures.
Last year's big Independence Day weekend movie release was Spider-Man 2, which took a record $40.5m (£22.5m) in the US on its opening day.
Spider-Man 2 went on to take £180.1m (£101.4m) in its first six days, and more than $370m (£208m) in total in the US alone.
The original Spider-Man grossed more than $820m (£448m) overall worldwide when it opened in 2002.