Guy Ritchie's take on the 1992 movie brought in more than $86m (£68m) in its first three days in North America.
The film, released on the US's four-day Memorial Day weekend, is expected to earn $105m (£83m) when Monday's ticket sales are included.
This would go well beyond earlier estimates of about $80 million (£63m).
The new version features Will Smith in the role of the blue Genie - formerly voiced by the late Robin Williams - and the Egyptian-born Canadian actor Mena Massoud as the wily charmer who pretends to be a prince to catch the attention of Jasmine, portrayed by Naomi Scott.
This time last year, Disney was reeling from a disappointing opening for Solo: A Star Wars Story, but with the Genie's help the company says it has raced ahead of opening weekend sales in the UK for both the Elton John biopic, Rocketman, and The Secret Life of Pets 2.