More than five million people have downloaded the latest version of Firefox since its release a day ago.
Mozilla, which makes the number two web browser, has been keeping a real-time map showing where in the world users are installing the software.
Despite the rapid uptake, downloads have been slower for version 4 than its predecessor.
Over the past year, Firefox's market share has declined slightly in the face of competition from Google's Chrome.
Firefox 4 was made available for download less than a month after Microsoft launched Internet Explorer 9, the latest version of its market-leading browser.
Both pieces of software promise users a faster, more secure online experience.
Firefox, like its rival, now makes extensive use of HTML 5 - the newest standard for the hypertext language used to build websites.
Both browsers also feature hardware acceleration for displaying web pages - drawing on the power of a computer's graphics processor to improve the speed of complex visuals