
The co-founders of Adobe have published an open letter in which they say that Apple threatens to "undermine the next chapter of the web".
The software firm has also started an adverting blitz in newspapers and on popular technology news sites.
Some of the online adverts contain the tongue-in-cheek slogan "We heart Apple".
It follows a letter from Apple boss Steve Jobs in which he defended his firm's decision not to allow Adobe's Flash technology on many of its popular products.
Mr Jobs described Adobe's software - used on many websites for video and animations - as a "closed system" and "100% proprietary".
"While Adobe's Flash products are widely available, this does not mean they are open, since they are controlled entirely by Adobe and available only from Adobe."
Whilst Mr Jobs admitted that Apple also had "many proprietary products", he said that Apple believed "all standards pertaining to the web should be open".
Amongst other criticisms, he also said Flash performed poorly when used on touchscreen smartphones and handheld devices.
Adobe co-founders Chuck Geschke and John Warnock have now hit back.
"We believe that consumers should be able to freely access their favorite content and applications, regardless of what computer they have, what browser they like, or what device suits their needs," the letter reads.
"No company - no matter how big or how creative - should dictate what you can create, how you create it, or what you can experience on the web."
'Smokescreen'
Adobe's campaign is the latest move in a high-profile war of words between the two companies, which began with Apple's decision not to allow Flash technology to run on some of its popular gadgets such as the iPhone and iPad.
But Flash is commonly used to build smartphone apps. As a result, developers commonly used automatic translation tools - some built by Adobe - to convert Flash code to run on Apple gadgets.
These allowed developers to make applications once and then distribute them for use on various phones and operating systems, including Apple's iPhone.
But in April, Apple changed the terms and conditions of the licence that software developers must sign, banning them from using these tools.
Mr Jobs justified the decision in his letter by saying that experience had shown that the tools resulted in "sub-standard apps".
The change effectively forced developers to build two separate applications - one for Apple products and one for everything else.
Adobe CEO Shantanu Narayen described Mr Job's letter as a "smokescreen" and said the decision had made it "cumbersome" for developers who were forced to have "two workflows".
Tongue-in-cheek
The new letter from the co-founders of Adobe attacks Mr Jobs' assertion that Flash is a closed system.
"As the founders of Adobe, we believe open markets are in the best interest of developers, content owners, and consumers."
"If the web fragments into closed systems, if companies put content and applications behind walls, some indeed may thrive - but their success will come at the expense of the very creativity and innovation that has made the internet a revolutionary force.
The company claims that its software- and particularly Flash - is open.
"We publish the specifications for Flash — meaning anyone can make their own Flash player," it reads.
"We believe that Apple, by taking the opposite approach, has taken a step that could undermine this next chapter of the web - the chapter in which mobile devices outnumber computers, any individual can be a publisher, and content is accessed anywhere and at any time.
"In the end, we believe the question is really this: Who controls the world wide web? And we believe the answer is: nobody — and everybody, but certainly not a single company."
In response to the letter, an Apple spokesperson said that the firm also believes in "open web standards" such as HTML5, the latest version of a programming language used to build web pages.
"Flash is not an open web standard like HTML. It is a proprietary Adobe product. Just ask the W3 consortium that controls web standards - they have chosen HTML5 as the open web standard to move forward with."
Adobe's letter has been published on its website as part of a global advertising campaign.
The adverts list a series of technologies that Adobe says it "loves".
It ends: "What we don't love is anybody taking away your freedom to choose what you create, how you create it, and what you experience on the web."
The adverts have been bought in the New York Times, Washington Post, San Francisco Chronicle as well as the Financial Times and Wall Street Journal. Online, they appear on Wired, Techcrunch and Engadget.