More than six million people have downloaded the latest version of Firefox since its release a day ago.
Visit Live Stats of Mozilla download here: www.glow.mozilla.orgMozilla, 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, one of main the programming languages used to build websites.
Both browsers feature hardware acceleration when displaying HTML 5 pages - drawing on the power of a computer's graphics processor to improve the speed of complex visuals.
Within its first 24 hours, more than 5.5 million users had downloaded Firefox 4. However, that falls short of the 8 million who downloaded version 3 on its release day in 2008.
The lower figure may be explained by the widespread availability of pre-release versions of Firefox 4 in the months ahead of its launch.
Firefox has enjoyed rapid growth since it first appeared in 2004. At its peak, in 2009 it held a 24% market share, according to Netmarketshare.
However, by February 2011 its slice of the browser market had fallen to 21%.
At the same time, Google's Chrome browser has grown from 1% to 10%, according to the same figures.
Internet Explorer remains the dominant platform, although its fall has been the most precipitous - from 68% in March 2009 to 56% in February 2011.
Some analysts believe that Firefox could still secure a bigger piece of the increasingly fragmented market, especially among corporate users.
"Internet Explorer 9 is only for Windows Vista and 7. Two thirds of companies are still using Windows XP," said Ovum analyst Richard Edwards.
"If you want to make the most of the HTML 5 stuff that is out there then you have to go to IE9 and a Windows 7 upgrade or switch to Firefox.
"That may be a significant opportunity for Firefox," he said.
Source: Mozilla and BBC news